Papers, 2005-Present (Warning: The file of the paper might not coincide with the published version). Work partly supported by NSF grants. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Books


  • Paternain, Gabriel; Salo, Miko; Uhlmann, Gunther
    Geometric Inverse Problems, With Emphasis in Two Dimensions
    Cambridge University Press (2023)

    • Books Edited


  • Inside-Out, Inverse Problems and Applications
    MSRI publication 47, Cambridge University Press (2003).

  • Inverse Problems and Applications
    Joint with G. Alessandrini
    Contemporary Math AMS, Volume 333 (2003).

  • Geometric Methods in Inverse Problems and boundary Control
    Joint with C. Croke, I. Lasieka and M. Vogelius
    IMA Publications, Vol. 137, Springer-Verlag (2004).

  • Partial Differential Equations and Inverse Problems
    Joint with C. Conca, R. Manasevich and M. Vogelius
    Contemporary Math 362 (2004).

  • Seminar on Inverse problems and Applications
    Co-Editor with G. Perla Menzala
    Special issue of Computational and Applied Mathematics, vol 25, no. 2-3 Petropolis. (2006)
    - This issue was dedicated to celebrate the 25 years of the foundation of LNCC and 25 years of the seminal paper of A. P. Calderon “On an inverse boundary value problem.”

  • Journal of Physics Conference Series Vol. 124
    Applied Inverse Problems, Theoretical and Computational Aspects (2008).

  • Methods and Applications of Analysis
    Co-Guest Editor with T.-S. Chung, M. Yamamoto and J. Zou
    Vol. 17 (2010) and Vol. 1 (2011).

  • Tomography and Inverse Transport Theory
    Co-Editor
    Contemporary Math Vol. 559 (2012).

  • Inside-Out, Vol II. MSRI Publications Vol. 60
    Cambridge University Press, 2012.

  • Special issue on complex geometrical optics (CGO) solutions
    Co-Editor
    Inverse Probl. Imaging 8 (2014), no. 4.

    • Preprints:


  • Kian, Yavar; Uhlmann, Gunther
    Determination of the sound speed and an initial source in photoacoustic tomography
    Preprint.


  • Lin, Ching-Lung; Lin, Yi-Hsuan; Uhlmann, Gunther
    The Calderón problem for nonlocal parabolic operators
    Preprint.


  • Lai, Ru-Yu; Uhlmann, Gunther; Zhou, Hanming
    Recovery of coefficients in semilinear transport equations
    Preprint.


  • Ilmavirta, Joonas; Uhlmann, Gunther
    Breaking the conformal invariance with supernova neutrino tomography
    Preprint.


  • Ghosh, Tuhin; Uhlmann, Gunther
    The Calderón problem for nonlocal operators
    Preprint.


  • Feizmohammadi, Ali; Ghosh, Tuhin; Krupchyk, Katya; Uhlmann, Gunther
    Fractional anisotropic Calderón problem on closed Riemannian manifolds
    Preprint.


  • Uhlmann, Gunther; Wang, Yiran
    The anisotropic Calderón problem for fixed high frequency
    Preprint.


  • Lassas, Matti; Uhlmann, Gunther; Wang, Yiran
    Determination of vacuum space-times from the Einstein-Maxwell equations
    Preprint.
     

  • Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
    Linearization Stability Results and Active Measurements for the Einstein-Scalar Field Equations
    Preprint.
     

  • Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
    Determination of structures in the space-time from local measurements: a detailed exposition.
    Preprint.
     

  • Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
    Comment on "Scattering Theory Derivation of a 3D Acoustic Cloaking Shell".
    Preprint.
     

    • To Appear:


  • Uhlmann, Gunther; Zhang, Yang
    An inverse boundary value problem arising in nonlinear acoustics
    To appear, SIAM J. Math Analysis


  • Uhlmann, Gunther; Wang, Yiran
    Recovery of black hole mass from a single quasinormal mode
    To appear, Comm. Math. Physics.


  • Quan, Hadrian; Uhlmann, Gunther
    The Calderón problem for the fractional Dirac operator
    To appear, Math. Research Letters.


  • Oksanen, Lauri; Salo, Mikko; Stefanov, Plamen; Uhlmann, Gunther
    Inverse Problems for Real Principal Type Operators
    To appear, American Journal of Math.
     

  • Krupchyk, Katya; Uhlmann, Gunther; Yan, Lili
    A remark on inverse problems for nonlinear magnetic Schrödinger equations on complex manifolds
    To appear, Proceedings of the American Math. Soc.


  • Krupchyk, Katya; Uhlmann, Gunther
    Inverse problems for nonlinear magnetic Schrödinger equations on conformally transversally anisotropic manifolds
    To appear, Analysis and PDE


  • Kian, Yavar; Krupchyk, Katya; Uhlmann, Gunther
    Partial data inverse problems for quasilinear conductivity equations
    To appear, Math. Annalen.


  • Feizmohammadi, Ali; Kian, Yavar; Uhlmann, Gunther
    An inverse problem for a quasilinear convection--diffusion equation
    To appear, Nonlinear Analysis


  • Uhlmann, Gunther; Zhou, Hanming
    Journey to the Center of the Earth
    To appear, Proceedings International Congress of Mathematical Physics, 2015.
     

    Published:


  • Kian, Yavar; Uhlmann, Gunther
    Recovery of nonlinear terms for reaction diffusion equations from boundary measurements
    Archive for Rational Mechanics and Analysis, 247 (2023), no. 1, 6.


  • Carstea, Catalin; Ghosh, Tuhin; Uhlmann, Gunther
    An inverse problem for the porous medium equation with a possibly absorption term
    SIAM J. Math. Analysis, 55 (2023), 162–185.


  • Uhlmann, Gunther; Zhang, Yang
    Inverse boundary value problems for wave equations with quadratic nonlinearities
    J. Differential Equations, 309 (2022), 558–607


  • Lai, Ru-Yu; Uhlmann, Gunther; Zhai, Gunther; Zhou, Hanming
    Single pixel X-ray transform and related inverse problems
    SIAM J. Imag. Sciences, 15 (2022), 1894–1909.


  • Kurylev, Yaroslav; Lassas, Matti; Oksanen, Lauri; Uhlmann, Gunther
    Inverse Problems for Einstein-Scalar Field Equations
    Duke Math. J., 171 (2022), 3215–3282.
     

  • Krupchyk, Katya; Salo, Mikko; Uhlmann, Gunther; Wang, Jenn-Nan
    On the scientific work of Victor Isakov
    Inverse Problems and Imaging, 16 (2022), 1429–1445.
     

  • Hintz, Peter; Uhlmann, Gunther; Zhai, Jian
    An inverse boundary value problem for a semilinear wave equation on Lorentzian manifolds
    International Math. Research Notices (IMRN), 17 (2022), 13181–13211.


  • Covi, Giovanni; Mönkkönen, Keijo; Railo, Jesse; Uhlmann, Gunther
    The Higher Order Fractional Calderón Problem for Linear Local Operators: Uniqueness
    Advances in Math, 399 (2022), 108246
     

  • Bhattacharyya, Sombuddha; de Hoop, Maarten; Katsnelson, Vitaly; Uhlmann, Gunther
    Recovery of piecewise smooth density and Lamé parameters from high-frequency exterior Cauchy data
    SIAM J. Imaging Sciences, 15 (2022), 1910–1943.


  • Bhattacharyya, Sombuddha; de Hoop, Maarten; Katsnelson, Vitaly; Uhlmann, Gunther
    Recovery of wave speeds and density of mass across a heterogeneous smooth interface from acoustic and elastic wave reflection operators
    GEM Int. J. Geomath., 13 (2022), no. 1, Paper No. 9, 46 pp.


  • Barreto, Antônio Sá; Uhlmann, Gunther; Wang, Yiran
    Inverse Scattering for Critical Semilinear Wave Equations
    Pure and Applied Analysis, 4 (2022), 191–223.
     

  • Acosta, Sebastian; Uhlmann, Gunther; Zhai, Jian
    Nonlinear ultrasound imaging modeled by a Westervelt equation
    SIAM J. Appl. Math, 82 (2022), 408-426.


  • Uhlmann, Gunther; Zhai, Jian
    On an Inverse Boundary Value Problem For A Nonlinear Elastic Wave Equation
    Journal des Mathematiques Pures et Appliquees, 153 (2021), 114-136.
     

  • Uhlmann, Gunther; Yang, Yang; Zhou, Hanming
    Travel Time Tomography in Stationary Spacetimes
    Journal of Geometric Analysis, 31 (2021), 9573 - 9596.
     

  • Stefanov, Plamen; Uhlmann, Gunther; Vasy, Andras
    The transmission problem in linear isotropic elasticity
    Pure and Applied Analysis, 3 (2021), 109-161.
     

  • Stefanov, Plamen; Uhlmann Gunther; Vasy, Andras
    Local and global boundary rigidity and the geodesic X-ray transform in the normal gauge
    Annals of Math., 194 (2021), 1-95.
     

  • Lai, Ru-Yu; Uhlmann, Gunther; Yang, Yang
    Reconstruction of the Collision Term in the Nonlinear Boltzmann Equation
    SIAM J. Math Analysis, 53, (2021), 1049 - 1069.
     

  • Kow, Pu-Zhao; Uhlmann, Gunther; Wang, Jenn-Nan
    Optimality of increasing stability for an inverse boundary value problem
    SIAM J. Math. Anal..bf 53 (2021), 7062–7080.
     

  • Feizmohammadi, Ali; Krupchyk, Katya; Oksanen, Lauri; Uhlmann, Gunther
    Reconstruction in the Calderón problem on conformally transversally anisotropic manifolds
    J. Functional Analysis, 281 (2021), 109191.


  • de Hoop, Maarten V.; Saksala, Teemu; Uhlmann, Gunther; Zhai, Jian
    Generic uniqueness and stability for mixed ray transforms
    Transaction of the AMS, 374 (2021), 6085-6144.
     

  • Caday, Peter; de Hoop, Maarten; Katsnelson, Vitaly; Uhlmann, Gunther
    Recovery of discontinuous Lamé parameters from local dynamic boundary data
    Comm. in PDE, 46(2021), 680-715.
     
  • Bhattacharyya, Sombuddha; Ghosh, Tuhin; Uhlmann, Gunther
    Inverse Problem for Fractional-Laplacian with Lower Order Non-local Perturbations
    Trans. Amer. Math. Soc., 374 (2021), 3053-3075.
     

  • Uhlmann, Gunther; Wang, Yiran
    Determination of space-time structures from gravitational perturbations
    Comm. Pure and Appl. Math., 73 (2020), 1315–1367
     

  • Uhlmann, Gunther; Wang, Yiran
    Convolutional neural networks in phase space and inverse problems
    SIAM J. Appl. Math., 80(6) (2020), 2560–2585. (26 pages)
     

  • Muńoz, Claudio; Uhlmann, Gunther
    The Calderón problem for quasilinear elliptic equations
    Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 37 (2020), 1143-1166
     

  • Lassas, Matti; Oksanen, Lauri; Stefanov, Plamen; Uhlmann, Gunther
    The Light Ray transform on Lorentzian manifolds
    Commun. Math. Phys. 377 (2020), 1349–1379.
     

  • Krupchyk, Katya; Uhlmann, Gunther
    Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities
    Mathematics Research Letters, 27 (2020), 1801-1824.
     

  • Krupchyk, Katya; Uhlmann, Gunther
    A remark on partial data inverse problems for semilinear elliptic equations
    Proc. Amer. Math. Soc. 148 (2020), 681-685
     

  • Ghosh, Tuhin; Salo, Mikko; Uhlmann, Gunther
    The Calderón problem for the fractional Schrödinger equation
    Anal. PDE 13 (2020), 455–475.
     

  • Ghosh, Tuhin; Rüland, Angkana; Salo, Mikko; Uhlmann, Gunther
    Uniqueness and reconstruction for the fractional Calderón problem with a single measurement
    Journal of Functional Analysis 279 (2020), 108505.
     

  • de Hoop, Maarten; Uhlmann, Gunther; Wang, Yiran
    Nonlinear interaction of waves in elastodynamics and an inverse problem
    Mathematische Annalen volume, 376 (2020), pages765–795
     

  • de Hoop, Maarten; Uhlmann, Gunther; Vasy, Andras
    Recovery of material parameters in transversely isotropic media
    Arch Rational Mech Anal, 235 (2020), 141–165
     

  • Paternain, Gabriel; Uhlmann, Gunther; Zhou, Hanming
    Lens rigidity for a particle in a Yang-Mills field
    Comm. Math. Phys. 366 (2019), 681–707.
     

  • Lai, Ru-Yu; Li, Qin; Uhlmann, Gunther
    Inverse problems for the stationary transport equation in the diffusion scaling
    SIAM J. Appl. Math., 79 (2019), 2340–2358.
     

  • Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
    Inverse Problems in Spacetime II: Reconstruction of a Lorentzian Manifold From Light Observation Sets
    International Math. Research Notices (IMRN), 22 (2019), 6949–6987
     

  • Krupchyk, Katya; Uhlmann, Gunther
    Stability estimates for partial data inverse problems for Schrödinger operators in the high frequency limit
    Journal des Math´ematiques Pures et Appliqu´ees, 126 (2019), 273–291.
     

  • Hintz, Peter; Uhlmann, Gunther
    Reconstruction of Lorentzian manifolds from boundary light observation sets
    International Math. Research Notices (IMRN), 22 (2019), 6949–6987.
     

  • Graham, C. Robin; Guillarmou, Colin; Stefanov, Plamen; Uhlmann, Gunther
    X-ray transform and boundary rigidity for asymptotically hyperbolic manifolds
    Annals of the Fourier Institute, Tome 69 No. 7 (2019), 2857-2919.
     

  • Deng, Youjun; Liu Hongyu; Uhlmann Gunther
    On an inverse boundary problem arising in brain imaging
    J. Differential Equations, 267 (2019), 2471–2502.
     

  • de Hoop, Maarten; Uhlmann, Gunther; Zhai, Jian
    Inverting the local geodesic ray transform of higher rank tensors
    Inverse Problems, 35 (2019), 115009.
     

  • de Hoop, Maarten; Uhlmann, Gunther; Wang, Yiran
    Nonlinear responses from the interaction of two progressing waves at an interface
    Annales de l'Institute Henri Poincar\'e, Analyse Non-Lin\'eaire., 36 (2019), 347-363.
     

  • Caday, Peter; De Hoop, Maarten; Katsnelson, Vitaly; Uhlmann, Gunther
    Reconstruction of piecewise smooth wave speeds using multiple scattering
    Trans. Amer. Math. Soc., 372 (2019), 1213-1235
     

  • Caday, Peter; De Hoop, Maarten; Katsnelson, Vitaly; Uhlmann, Gunther
    Scattering Control for the Wave Equation with Unknown Wave Speed
    Archive for Rational Mechanics and Analysis, 231(2019), 409-464.
     

  • Au Yeung, Tak Shing; Chung, Eric T.; Uhlmann, Gunther
    Numerical inversion of 3D geodesic X-ray transform arising from traveltime tomography
    SIAM J. Imaging Sci., 12(3) (2019), 1296–1323.
     

  • Stefanov, Plamen; Uhlmann, Gunther; Vasy, Andras
    Inverting the local geodesic X-ray transform on tensors
    Journal D’Analyse Math., 136 (2018), 151–208.
     

  • Krupchyk, Katya; Uhlmann, Gunther
    Inverse problems for magnetic Schrödinger operators in transversally anisotropic geometries
    Comm. Math. Phys., 361 (2018), 525–582.
     

  • Krupchyk, Katya; Uhlmann, Gunther
    Inverse problems for advection diffusion equations in admissible geometries
    Comm in PDE, 43 (2018), 585–615.
     

  • Greenleaf, Allan; Lassas, Matti; Santacesaria, Matteo; Siltanen, Samuli; Uhlmann, Gunther
    Propagation and recovery of singularities in the inverse conductivity problem
    Analysis and PDE, 11(2018), 1901-1943
     

  • Ilmavirta, Joonas; Uhlmann, Gunther
    Tensor tomography in periodic slabs
    Journal of Functional Analysis 275 (2018), no. 2, 288–299.
     

  • Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther;
    Inverse problems for Lorentzian manifolds and non-linear hyperbolic equations
    Invent. Math. 212 (2018), no. 3, 781–857.
     

  • Lassas, Matti; Uhlmann, Gunther; Wang, Yiran
    Inverse problems for semilinear wave equations on Lorentzian manifolds
    Comm. Math. Physics. 360 (2018), no. 2, 555–609.
     

  • Holman, Sean; Uhlmann, Gunther
    On the microlocal analysis of the geodesic X-ray transform with conjugate points
    Journal of Differential Geometry 108 (2018), no. 3, 459–494.
     

  • Lassas, Matti; Oksanen, Lauri; Stefanov, Plamen; Uhlmann, Gunther
    On the inverse problem of finding cosmic strings and other topological defects
    Comm. Math. Physics. 357 (2018), no. 2, 569–595.
     

  • Assylbekov, Yernat; Monard, Francois; Uhlmann, Gunther
    Inversion formulas and range characterizations for the attenuated geodesic ray transform
    Journal de Mathematiques Pures et Appliquees. (9) 111 (2018), 161–190.
     

  • Greenleaf, Allan; Kettunen, Henrik; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
    Superdimensional Metamaterial Resonators from sub-Riemannian geometry
    SIAM J. Appl. Math. 78 (2018), no. 1, 437–456.
     

  • Stefanov, Plamen; Uhlmann Guntheri; Vasy, Andras
    Local recovery of the compressional and shear speeds from the hyperbolic DN map
    Inverse Problems 34 (2018), no. 1, 014003.
     

  • Krupchyk, Katya; Uhlmann, Gunther
    Bounds on eigenfunctions of semiclassical operators with double characteristics
    Asymptot. Anal. 106 (2018), no. 1, 25–46.
     

  • Palacios, Benjamin; Uhlmann, Gunther; Wang, Yiran
    Quantitative analysis of metal artifacts in X-ray tomography
    SIAM J. Math. Anal., 30 (2018), 4914-4936.
     

  • Palacios, Benjamin; Uhlmann, Gunther; Wang, Yiran
    Reducing Streaking Artifacts in Quantitative Susceptibility Mapping
    SIAM J.Imaging Science. 10 (2017), no. 4, 1921–1934.
     

  • Lai, Ru-Yu; Shankar, Ravi; Spirn, Daniel; Uhlmann Gunther
    An inverse problem from condense matter physics
    Inverse Problems 33 (2017), no. 11, 115011
     

  • Deng, Youjun; Liu, Hongyu; Uhlmann, Gunther
    On regularized full- and partial-cloaks in acoustic scattering
    Comm. PDE. 42(2017), 821-851.
     

  • Deng, Youjun; Liu, Hongyu; Uhlmann, Gunther
    Full and Partial Cloaking in Electromagnetic Scattering
    Arch. Ration. Mech. Anal. 223 (2017), 265–299.
     

  • Krupchyk, Katya; Uhlmann, Gunther
    Absolute Continuity of the Periodic Schrödinger Operator in Transversal Geometry
    J. Eur. Math. Soc. (JEMS) 19 (2017), 531–550.
     
  • Uhlmann, Gunther; Vasy, Andras
    The Inverse Problem for the Local Geodesic X-ray Transform.
    Inventiones Mathematicae 205 (2016) 83–120
     
  • Sj\"ostrand, J.; Uhlmann Gunther
    Local Analytic Regularity for the Linearized Calderon Problem
    Analysis & PDE, 9 (2016), 515-544.
     
  • Stefanov, Plamen; Uhlmann Guntheri; Vasy, Andras
    Boundary Rigidity with Partial Data
    Journal of the AMS 29 (2016), 299–332.
     
  • Stefanov, Plamen; Uhlmann, Gunther; Vasy, Andras
    On the stable recovery of a metric from the hyperbolic DN map with incomplete data
    Inverse Probl. Imaging 10 (2016), 1141–1147.
     

  • Paternain, Gabriel; Salo, Mikko; Uhlmann, Gunther; Zhou, Hanming
    The geodesic X-ray transform with matrix weights
    American Journal of Mathematics, 141(6) (2016)
     

  • Krupchyk, Katya; Uhlmann, Gunther
    Inverse Boundary Problems for Polyharmonic Operators with Unbounded Potentials
    J. Spectral Theory, 6 (2016), 145-183.
     

  • Krupchyk, Katya; Uhlmann, Gunther
    The Calderon problem with partial data for conductivities with 3/2 derivatives
    Comm. Math. Phys. 348 (2016), 185–219.
     

  • Guillarmou, Colin; Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther
    The X-ray transform for connections in negative curvature
    Comm. Math. Phys. 343 (2016), 83–127.
     

  • Bal, Guillaume; Monard, Francois; Uhlmann, Gunther
    Reconstruction of a fully anisotropic elasticity tensor from knowledge of displacement fields
    SIAM J. Appl. Math. 75 (2015), 2214–2231
     

  • De Hoop Maarten; Uhlmann, Gunther; Vasy, Andras
    Difraction by conormal singularities
    Annales Scientifiques de l'Ecole Normale Superieure, 48 (2015), 351--408.
     
  • Imanuvilov, Oleg; Uhlmann, Gunther; Yamamoto Masahiro
    The Neumann-to-Dirichlet map in two dimensions.
    Adv. Math. 281 (2015), 578–593.
     
  • Krupchyk, Katya; Uhlmann, Gunther
    On Lp Resolvent Estimates for Elliptic Operators on Compact Manifolds
    Comm. PDE, 40 (2015), 438-474.
     
  • Lai, Ru-Yu; Uhlmann, Gunther;Wang, Jenn-Nan
    Inverse Boundary Value Problem for the Stokes and the Navier-Stokes Equations in the Plane
    Arch. Ration. Mech. Anal. 215 (2015), 811-829
     
  • Li, Jongzhi; Liu, Hongyu; Rondi, Luca; Uhlmann, Gunther
    Regularized Transformation-Optics Cloaking for Helmholtz Equation: From Partial Cloak to Full Cloak.
    Comm. Math. Phys., 335 (2015), 671--712
     
  • Liu, Hongyu; Uhlmann, Gunther
    Determining both sound speed and internal source in thermo- and photo-acoustic tomography
    Inverse Problems 31 (2015), 105005.
     

  • Liu, Hongyu; Uhlmann, Gunther
    Regularized Transformation-Optics Cloaking in Acoustic and Electromagnetic Scattering
    Inverse Problems and Imaging, Société mathématique de France, Panoramas et Syntheses, 44, (2015), 111-136.
     

  • Monard, Francois; Stefanov, Plamen; Uhlmann Gunther
    The Geodesic Ray Transform on Riemannian Surfaces with Conjugate Points
    Comm. in Mathematical Physics, 337, 1491--1513 (2015)
     
  • Paternain, Gabriel; Salo, Mikko; Uhlmann Gunther
    Invariant Distributions, Beurling Transform and Tensor Tomography in Higher Dimensions
    Math. Ann. 363 (2015), 305–362.
     
  • Paternain, Gabriel; Salo, Mikko; Uhlmann Gunther
    On the Range of the Attenuated Ray Transform for Unitary Connections.
    Int. Math. Res. Not. IMRN (2015), 873–897.
     
  • Pestov, Leonid; Uhlmann, Gunther; Zhou, Hanming
    An Inverse Kinematic Problem with Internal Sources
    Inverse Problems 31 055006 (2015)
     

  • Rakesh; Uhlmann Gunther
    The Point Source Inverse Back-Scattering Problem
    Contemporary Math., 644 (2015), 279-289.
     
  • Uhlmann, Gunther; Zhou, Ting
    Inverse Electromagnetic Problems.
    Encyclopedia of Applied and Computational Mathematics (2015) 716-725, Springer-Verlag, edited by B. Enquist.
     
  • Isakov, V., Nagayasu Sei; Uhlmann, Gunther;Wang, Jenn-Nan
    Increasing Stability of the Inverse Boundary Value Problem for the Schroedinger Equation`.
    Contemp. Math. 615 (2014), 131-141.
     
  • Krupchyk, Katya; Uhlmann, Gunther
    Determining a magnetic Schr\"odinger operator with a bounded magnetic potential from boundary measurements
    Comm. Math. Phys., 327 (2014), 993-1009.
     
  • Krupchyk, Katya; Lassas, Matti; Uhlmann, Gunther
    Inverse Boundary value Problems for the Perturbed Polyharmonic Operator
    Transactions AMS, 366 (2014), 95-112.
     
  • Oksanen Lauri; Uhlmann Gunther
    Photoaocustic and Thermoacoustic Tomography with an Uncertain Wave Speed
    Math. Research letters 21 (2014) 1199-1214
     
  • Paternain, Gabriel; Salo, Mikko; Uhlmann Gunther
    Spectral Rigidity and Invariant Distributions on Anosov Manifolds.
    J. Differential Geom. 98 (2014), 147–181.
     
  • Paternain, Gabriel; Salo, Mikko; Uhlmann Gunther
    Tensor Tomography in Two Dimensions:Progress and Challenges.
    . Chinese Annals of Math. Ser. B, Ser. B, 35 (2014), 399-427.
     
  • Rakesh; Uhlmann Gunther
    Uniqueness in the Backscattering Problem for Angularly Controlled Potentials
    Inverse Problems, 30 (2014) 065005
     
  • Uhlmann, Gunther
    30 years of Calderón's problem.
    Séminaire Laurent Schwartz—Équations aux dérivées partielles et applications. Année 2012–2013, Exp. No. XIII, 25 pp., Sémin. Équ. Dériv. Partielles, École Polytech., Palaiseau, (2014).
     
  • Albin, Pierre; Guillarmou, Colin, Tzou, Leo; Uhlmann, Gunther
    Inverse boundary problems for systems in two dimensions
    Annales Intitut Henri Poincar\'e, 14 (2013), 1551-1571.
     
  • Bal, Guillaume; Uhlmann, Gunther
    Reconstruction of coefficients in scalar second order elliptic equations from knowledge of their solutions.
    Comm. on Pure and Applied Math., 66 (2013), 1692-1652.
     
  • De Hoop Maarten; Uhlmann, Gunther; Vasy, Andras; Wendt, H.,
    Multi-scale discrete approximations of Fourier integral operators.
    SIAM Multiscale Modeling and Simulation, 11 (2013), 566-585. .
     
  • Nagayasu Sei; Uhlmann, Gunther;Wang, Jenn-Nan
    Increasing Stability in an Inverse Problem for the Acoustic Equation.
    Inverse Problems, 29 (2013), 229-247.
     
  • Paternain, Gabriel; Salo, Mikko; Uhlmann Gunther
    Tensor Tomography on Simple Surfaces.
    Inventiones Math., 193 (2013), 229-247.
     
  • Stefanov, Plamen; Uhlmann Gunther
    Is a Curve Flight Path in SAR Better than a Straight One?
    SIAM J. Appl. Math., 73 (2013), 1596-1612.
     
  • Stefanov, Plamen; Uhlmann Gunther
    Recovery of a Source or a Speed with One Measurement and Applications
    Transactions AMS., 365 (2013), 5737-5758.
     
  • Stefanov, Plamen; Uhlmann Gunther
    Instability for the Linearized Problem in Multiwave Tomography of Recovery Both the Source and the Speed.
    Inverse Problems and Imaging, 7 (2013), 1367-1377.
     
  • Bal, Guillaume; Uhlmann, Gunther
    Reconstructions for some coupled physics problems.
    Applied Mathematics Letters, 25 (2012), 1030-1033.
     
  • De Hoop, Maarten; Holman, Sean; Smith, Hart; Uhlmann Gunther
    Regularity and Multi-Scale Discretization of the Solution Construction of Hyperbolic Evolution Equations with Limited Smoothness.
    Applied and Computational Harmonic Analysis, 33 (2012), 330-353.
     
  • Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Leonhardt Ulf, Uhlmann, Gunther
    Schroedinger's Hat: Approximate Electromagnetic, Acoustic and Quantum Amplifiers Via Transformation Optics.
    Proceedings National Academy of Sciences (PNAS), 109 (2012), 10169-10174.
     
  • Imanuvilov, Oleg; Uhlmann, Gunther; Yamamoto Masahiro
    On Reconstruction of Lam\'e Parameters from Partial Cauchy Data in Three Dimensions.
    Inverse Problems, 28 (2012), 125002.
     
  • Imanuvilov, Oleg; Uhlmann, Gunther; Yamamoto Masahiro
    Partial Cauchy Data for General Second Order Elliptic Operators in Two Dimensions.
    Publ. Research Insti. Math. Sci, 48 (2012), 971-1055.
     
  • Krupchyk, Katya; Lassas, Matti; Uhlmann, Gunther
    Determining a First Order Perturbation of the Biharmonic Operator by Partial Boundary Measurements
    Journal Functional Analysis, 262 (2012), 1781-1801.
     
  • Krupchyk, Katya; Lassas, Matti; Uhlmann, Gunther
    Inverse Problems with Partial Data for a Magnetic Schroendinger Operator in an Infinite Slab or Bounded Domain
    Comm. Math. Phys., 312 (2012), 87-126.
     
  • Paternain, Gabriel; Salo, Mikko; Uhlmann Gunther
    The Attenuated Ray Transform for Connections and Higgs Fields.
    Geometric and Functional Analysis (GAFA), 22 (2012), 1460-1480.
     
  • Stefanov, Plamen; Uhlmann, Gunther
    Multi-wave methods via ultrasound
    Inverse Poblems and Applications, Inside Out II, MSRI Publications 60, C ambridge University Press (2012), 271-323 (ed. by G. Uhlmann).
     
  • Agarwal, W; Chen, Xudong; Hu, L.; Liu, Hongyu, Uhlmann Gunther
    Polarization Invariant Directional Cloaking by Transformation Optics.
    Progress In Electromagnetics Research, Vol. 118 (2011), 415-423. Comm. Math. Phys., 312 (2012), 87-126.
     
  • Paternain, Gabriel; Salo, Mikko; Uhlmann Gunther
    The Attenuated Ray Transform for Connections and Higgs Fields.
    Geometric and Functional Analysis (GAFA), 22 (2012), 1460-1480.
     
  • Stefanov, Plamen; Uhlmann, Gunther
    Multi-wave methods via ultrasound
    Inverse Poblems and Applications, Inside Out II, MSRI Publications 60, C ambridge University Press (2012), 271-323 (ed. by G. Uhlmann).
     
  • Agarwal, W; Chen, Xudong; Hu, L.; Liu, Hongyu, Uhlmann Gunther
    Polarization Invariant Directional Cloaking by Transformation Optics.
    Progress In Electromagnetics Research, Vol. 118 (2011), 415-423.
     
  • Chen, Xudong; Uhlmann Gunther
    Cloaking a Sensor for Three Dimensional Maxwell's Equations: A Transformation Optics Approach.
    Optics Express, 19 (2011), 20518-20530.
     
  • Imanuvilov, Oleg; Uhlmann, Gunther; Yamamoto Masahiro
    Inverse Boundary Problem with Cauchy data on Disjoint Sets.
    Inverse Problems, 27 (2011), 085007.
     
  • Qian Jianliang; Stefanov, Plamen; Uhlmann, Gunther; Zhao, Hong-Kai
    An Efficient Neumann-series Based Algorithm for the Thermoacoustic and Photoacoustic Tomography with Variable Sound Speed
    SIAM J. Imaging Sciences, 4 (2011), 850-883.
     

  • Chung, Eric; Qian Jianling; Uhlmann, Gunther; Zhao, Hong-Kai
    An Adaptive Method in Phase Space with Application to Reflection Travel Time Tomography
    Inverse Problems, 27 (2011) 115002.
     

  • Kenig, Carlos; Salo, Mikko; Uhlmann, Gunther
    Reconstruction from Boundary Measurements for Admissible Manifolds
    Inverse Problems and Imaging, 5 (2011), 859 - 877.
     

  • Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
    Cloaking a Sensor via Transformation Optics
    Physical Review E, 83 (2011), 016603.
     
  • Imanuvilov, Oleg; Uhlmann, Gunther; Yamamoto Masahiro
    Partial Cauchy Data for General Second Order Elliptic Operators in Two Dimensions.
    Publ. Research Insti. Math. Sci, 48 (2012), 971-1055.
     
  • Imanuvilov, Oleg; Uhlmann, Gunther; Yamamoto Masahiro
    On Determination of Second Order Elliptic Operators from Partial Cauchy Data.
    Proceedings National Academy of Sciences, 108 (2011), 467-472.
     
  • Bal, Guillaume; Ren, Kui, Uhlmann, Gunther; Zhou, Ting
    Quantitative Thermoacoustics and Related Topics.
    Inverse Problems, 27 (2011), 055007.
     
  • Stefanov, Plamen; Uhlmann Gunther
    Thermoacoustic Tomography Arising in Brain Imaging
    Inverse Problems, 27 (2011), 045004.
     
  • Brytik Valeriy; De Hoop Maarten; Smith, Hart; Uhlmann Gunther
    The Elastic Wave Equation of Limited Smoothness
    Comm. PDE., 36 (2011), 1683-1693.
     
  • Lin, Ching-Lung; Uhlmann, Gunther;Wang, Jenn-Nan
    Asymptotic Behavior of Solutions of the Stationary Navier Stokes Equation in Exterior Domains
    Indiana Math. J., 60 (2011), 2093-2106.
     
  • Salo, Mikko; Uhlmann, Gunther
    The Attenuated Ray Transform on Simple Surfaces
    J. Diff. Geometry, 88 (2011), 161-187.
     
  • Lassas, Matti; Salo, Mikko; Uhlmann, Gunther
    Wave Imaging
    Handbook of Mathematical Methods in Imaging, Springer-Verlag, O. Scherzer (Ed.), 2011.
     
  • Lin, Ching-Lung; Nakamura, Gen; Uhlmann, Gunther;Wang, Jenn-Nan
    Quantitative Unique continuation for the Lame System with Less Regular Coefficients
    Methods and Applications of Analysis, 18 (2011), 85-92.
     
  • Krupchyk, Katya; Lassas, Matti; Uhlmann, Gunther
    Inverse Problems for Differential Forms on Riemannian Manifolds with Boundary
    Comm. PDE, 36 (2011), 1475-1509.
     
  • Stefanov, Plamen; Uhlmann Gunther
    The Geodesic X-Ray Transform with Fold Caustics
    Anal. and PDE., 5 (2012), 219-260.
     
  • Lin, Ching-Lung; Uhlmann, Gunther;Wang, Jenn-Nan
    Optimal Three-Ball Inequalities and Quantitative Uniqueness for the Stokes system
    DCDS-A (Special issue dedicated to Professor Louis Nirenberg on the occasion of his 85th birthday), Vol 28 (2010), 1273-1290.
     
  • Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
    Approximate Acoustic and Quantum Cloaking
    Journal Spectral Theory, 1 (2011), 27-80.
     
  • Kenig, Carlos; Salo, Mikko; Uhlmann, Gunther
    Inverse Problems for the Anisotropic Maxwells Equations
    Duke Math. J., 157 (2011), 369-419.
     
  • Nagayasu Sei; Uhlmann, Gunther;Wang, Jenn-Nan
    Reconstruction of Penetrable Obstacles in Acoustics
    SIAM J. Math. Anal., 43 (2011), 189-211.
     
  • Bal, Guillaume; Uhlmann, Gunther
    Inverse Diffusion Theory of Photoacoustics.
    Inverse Problems, 26(2010), 085010.
     
  • Dairbekov Nurlan; Uhlmann, Gunther
    Reconstructing the Metric and Magnetic Field from the Scattering Relation
    Inverse Problems and Imaging, 4(2010), 397-409.
     
  • Imanuvilov, Oleg; Uhlmann, Gunther; Yamamoto Masahiro
    The Calderon Problem with Partial Data in Two Dimensions.
    Journal American Math. Society, 23(2010), 655-691.
     
    Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
    Rigidity of Broken Geodesic Flow and Inverse Problems
    American Journal of Math, 132(2010), 529-562.
     

  • Li, Xiaosheng; Uhlmann, Gunther
    Inverse Problems on a Slab
    Inverse Problems and Imaging, 4(2010), 449-462.
     
  • Paivarinta, Lassi; Salo, Mikko; Uhlmann, Gunther
    Inverse Scattering for the Magnetic Schroedinger Equation
    J. Funct. Anal. 259, (2010), 1771-1798.
     
  • Dos Santos Ferreira D.; Kenig C.; Sj\"ostrand, J.; Uhlmann Gunther
    On the Linearized Local Calderon Problem,
    Math Research Letters, 16(2009), 955-970.
     
  • Dos Santos Ferreira, David; Kenig, Carlos; Salo, Mikko; Uhlmann, Gunther
    Limiting Carleman Weights and Anisotropic Inverse Problems.
    Inventiones Math, 178(2009), 119-171.
     
  • De Hoop Maarten; Smith, Hart; Uhlmann Gunther; Van der Hilst Rob
    Seismic Imaging with the Generalized Radon Transform: A Curvelet Transform Perspective
    Inverse Problems 25 (2009) 025005
     
  • Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
    Cloaking Devices, Electromagnetic Wormholes and Transformation Optics
    SIAM Review 51 (2009), 3-33.
     
  • Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
    Invisibility and Inverse Problems
    Bulletin AMS 46 (2009), 55-97.
     
  • Nagayasu Sei; Uhlmann, Gunther;Wang, Jenn-Nan
    Depth Dependent Stability estimates in Electrical Impedance Tomography
    Inverse Problems 25 (2009), 075001.
     
  • Stefanov, Plamen; Uhlmann Gunther
    Thermoacoustic Tomography with Variable Sound Speed
    Inverse Problems, 25 (2009), 075011.
     
  • Stefanov, Plamen; Uhlmann Gunther
    Linearizing Non-linear Inverse Problems and its Applications to Inverse Backscattering
    Journal Functional Analysis 256 (2009), 2842-2866.
     
  • Stefanov, Plamen; Uhlmann Gunther
    Local Lens Rigidity with Incomplete Data for a Class of Non-Simple Riemannian Manifolds
    Journal Diff. Geometry 82 (2009), 383-409.
     
  • Uhlmann, Gunther
    Calderon's Problem and Electrical Impedance Tomography.
    Inverse Problems, 25th Anniversary Volume, 25(2009), 123011 (39pp.)
     
  • Uhlmann, Gunther
    Visibility and Invisibility.
    in 6th International Congress on Industrial.and Appl. Math. (ICIAM) -- Zurich, Switzerland, 16-20 July 2007 -- Invited Lectures, R. Jeltsch and G. Wanner eds, Euro Math Soc.(2009), 381-408.
     
  • Uhlmann, Gunther; Wang, Jenn-Nan
    Unique Continuation Property with General Residual Stress
    Inverse Problems and Imaging 3 (2009), 309-317.
     
  • Uhlmann, Gunther; Wang, Jenn-Nan; Wu, Chin-Tien
    Reconstruction of Inclusions in an Elastic Body
    Journal de Mathematiques Pures et Appliquees (2009), 569-582.
     
  • Andersson, Frederik; De Hoop Maarten; Smith, H.; Uhlmann Gunther
    A Multi-Scale Approach to Hyperbolic Equations with Limited Smoothness
    Comm. P.D.E., 33 (2008), 988-1017
     
  • Chung, Eric; Qian Jianling; Uhlmann, Gunther; Zhao, Hong-Kai
    A Phase-space Formulation for Elastic-wave Traveltime Tomography
    Journal of Physics: Conference Series 124 (2008), 012018.
     

  • Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
    Approximate Quantum Cloaking and Almost Trapped States
    Physical Review Letters 101 (2008), 220404.
     
  • Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
    Isotropic Transformation Optics: Approximate Acoustic and Quantum Cloaking
    New Journal of Physics 10 (2008), 115024-115051.
     
  • Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
    Inverse Problems, Invisibility, and Artificial Wormholes
    Journal of Physics: Conference Series 124 (2008), 012005.
     
  • Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
    Electromagnetic Wormholes via Handlebody Constructions
    Communications in Mathematical Physics, 281 (2008), 369-385
     

  • Melrose, Richard; Uhlmann, Gunther
    Generalized Backscattering and the Lax-Phillips Transform
    Serdica Math. J. 34 (2008), 1026-1044
     

  • Stefanov, Plamen; Uhlmann Gunther
    An Inverse Problem in Optical Molecular Imaging
    Analysis and PDE 1 (2008), 115-126.
     
  • Stefanov, Plamen; Uhlmann Gunther
    The X-Ray Transform for a Generic Family of Curves and Weights
    J. Geom. Anal. 18(1)(2008), 81-97
     
  • Stefanov, Plamen; Uhlmann Gunther
    Integral Geometry of Tensor fields on a Class of Non-Simple Riemannian Manifolds
    American J. of Math., 130 (2008), 239-268.
     
  • Stefanov, Plamen; Uhlmann Gunther
    Boundary and Lens Rigidity, Tensor Tomography, and Analytic Microlocal Analysis
    Algebraic Analysis of Differential Equations. In honor of Prof. Takahiro Kawai on the occasion of his 65th birthday. Aoki, T.; Takei, Y.; Tose, N.; Majima, H. (Eds.) (2008), Springer, pages 275-293.
     
  • Uhlmann, Gunther
    Commentary on Calder\'on's paper (29) ``On an inverse boundary value problem".
    Selected Papers of A.P. Calder\'on, edited by Alexandra Bellow, Carlos Kenig and Paul Malliavin, AMS (2008), 623-636.
     

  • Uhlmann, Gunther;Wang, Jenn-Nan
    Complex Geometrical Optics Solutions and Reconstruction of Discontinuities
    SIAM J. Appl. Math., 68 (2008), 1026-1044.
     
  • Chung, Eric; Qian Jianling; Uhlmann, Gunther; Zhao, Hong-Kai
    A New Phase Space Method for Recovering Index of Refraction from Travel Times
    Inverse Problems 23 (2007), no. 1, 309--329.
     

  • Dairbekov, Nurlan; Partenain, Gabriel; Stefanov, Plamen; Uhlmann Gunther
    The Boundary Rigidity Problem in the Presence of a Magnetic Field
    Adv. Math. 216(2)(2007), 535-609.
     
  • Dos Santos Ferreira D.; Kenig C.; Sj\"ostrand, J.; Uhlmann Gunther
    Determining the Magnetic Schr\"odinger Operator from Partial Cauchy Data.
    Comm. Math. Phys. 271 (2007), no. 2, 467--488.
     
  • Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
    Effectiveness and Improvement of Cylindrical Cloaking with the SHS Lining
    Optics Express, Vol. 15, Issue 20, pp. 12717-12734 (2007)
     

  • Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
    Electromagnetic Wormholes and Virtual Magnetic Monopoles from Metamaterials
    Physical Review Letters, 99, no. 18, 183901 (2007)
     

  • Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
    Full Wave Invisibility of Active Devices at all Frequencies
    Communications in Mathematical Physics, 275, no. 3 (2007), 749-789.
     

  • Horst Heck; Uhlmann, Gunther;Wang, Jenn-Nan
    Reconstruction of Obstacles Immersed in an Incompressible Fluid
    Inverse Probl. Imaging 1 (2007), no. 1, 63--76.
     
  • Ide T.; Isozaki, H.; Nakata S.; Siltanen S.; Uhlmann Gunther
    Probing for electrical inclusions with complex spherical waves.
    Communications on Pure and Applied Mathematics 60 (2007), pp. 1415-1442
     
  • Kenig C.; Sj\"ostrand, J.; Uhlmann Gunther
    The Calder\'on Problem with Partial Data.
    Ann. of Math. (2) 165 (2007), no. 2, 567--591.
     
  • Nolan, Clifford; Uhlmann, Gunther
    Parametrices for systems with multiplicity
    Wave Motion 44 (2007), no. 4, 231--247.
     
  • Takuwa Hideki; Uhlmann, Gunther; Wang, Jenn-Nan
    Complex Geometrical Optics Solutions for Anisotropic Equations and Applications
    J. Inv. Ill-Posed Problems 16 (2007), 791-804.
     
  • Uhlmann, Gunther;Wang, Jenn-Nan
    Complex spherical waves for the elasticity system and probing of inclusions
    SIAM J. Math. Anal. 38 (2007), no. 6, 1967--1980.
     
  • Uhlmann, Gunther; Wang, Jenn-Nan
    Reconstructing Discontinuities in Systems
    Journal of Physics: Conference Series (2007), 012024.
     
  • De Hoop M.; Uhlmann Gunther
    Characterization and source-receiver continuation of seismic reflection data
    Comm. Math. Physics, 263(2006), 1-19.
     
  • Nakamura, Gen; Uhlmann, Gunther;Wang, Jenn-Nan
    Oscillating Decaying Solutions for Elliptic Systems,
    Contemporary Math., 408(2006), 219-230. .
     
  • Pestov, Leonid; Uhlmann, Gunther
    The Scattering Relation and the Dirichlet-to-Neumann Map
    Contemporary Math, 412(2006), 249-262.
     
  • Nakamura, Gen; Uhlmann, Gunther;Wang, Jenn-Nan
    Oscillating Decaying Solutions, Runge Approximation and its Applications to Inverse Problems
    Journal de Mathematiques Pures et Appliquees, 85(2005), 21-54.
     
  • Pestov, Leonid; Uhlmann, Gunther
    Two Dimensional Compact Simple Riemannian manifolds are Boundary Distance Rigid
    Annals of Math., 161(2005), 1089-1106.
     
  • Nakamura, Gen; Uhlmann, Gunther;Wang, Jenn-Nan
    Reconstruction of Cracks in an Inhomogeneous Anisotropic Medium Using Point Sources
    Advances in Appl. Math., 34 (2005),591--615.
     
  • Sharafutdinov, Vladimir; Skokan, Michal; Uhlmann, Gunther
    Regularity of Ghosts in Tensor Tomography
    Journal of Geometric Analysis, 15 (2005), 499-542.
     
    `
  • Stefanov, Plamen; Uhlmann Gunther
    Boundary Rigidity and Stability for Generic Simple Metrics,
    Journal Amer. Math. Soc. 18(2005), 975-1003.
     
  • Stefanov, Plamen; Uhlmann Gunther
    Stable Determination of Generic Simple Metrics from the Hyperbolic Dirichlet-to-Neumann Map
    International Math. Research Notices, 17(2005), 1047-1061.