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
Geometric Inverse Problems, With Emphasis in Two Dimensions
Cambridge University Press (2023)
Books Edited
MSRI publication 47, Cambridge University Press (2003).
Joint with G. Alessandrini
Contemporary Math AMS, Volume 333 (2003).
Joint with C. Croke, I. Lasieka and M. Vogelius
IMA Publications, Vol. 137, Springer-Verlag (2004).
Joint with C. Conca, R. Manasevich and M. Vogelius
Contemporary Math 362 (2004).
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.”
Applied Inverse Problems, Theoretical and Computational Aspects (2008).
Co-Guest Editor with T.-S. Chung, M. Yamamoto and J. Zou
Vol. 17 (2010) and Vol. 1 (2011).
Co-Editor
Contemporary Math Vol. 559 (2012).
Cambridge University Press, 2012.
Co-Editor
Inverse Probl. Imaging 8 (2014), no. 4.
Preprints
Determination of the sound speed and an initial source in photoacoustic tomography
Preprint.
The Calderón problem for nonlocal parabolic operators
Preprint.
Recovery of coefficients in semilinear transport equations
Preprint.
Breaking the conformal invariance with supernova neutrino tomography
Preprint.
The Calderón problem for nonlocal operators
Preprint.
Fractional anisotropic Calderón problem on closed Riemannian manifolds
Preprint.
The anisotropic Calderón problem for fixed high frequency
Preprint.
Determination of vacuum space-times from the Einstein-Maxwell equations
Preprint.
Linearization Stability Results and Active Measurements for the Einstein-Scalar Field Equations
Preprint.
Determination of structures in the space-time from local measurements: a detailed exposition.
Preprint.
Comment on "Scattering Theory Derivation of a 3D Acoustic Cloaking Shell".
Preprint.
Articles (to appear)
An inverse boundary value problem arising in nonlinear acoustics
To appear, SIAM J. Math Analysis
Recovery of black hole mass from a single quasinormal mode
To appear, Comm. Math. Physics.
The Calderón problem for the fractional Dirac operator
To appear, Math. Research Letters.
Inverse Problems for Real Principal Type Operators
To appear, American Journal of Math.
A remark on inverse problems for nonlinear magnetic Schrödinger equations on complex manifolds
To appear, Proceedings of the American Math. Soc.
Inverse problems for nonlinear magnetic Schrödinger equations on conformally transversally anisotropic manifolds
To appear, Analysis and PDE
Partial data inverse problems for quasilinear conductivity equations
To appear, Math. Annalen.
An inverse problem for a quasilinear convection--diffusion equation
To appear, Nonlinear Analysis
Journey to the Center of the Earth
To appear, Proceedings International Congress of Mathematical Physics, 2015.
Articles (published)
Recovery of nonlinear terms for reaction diffusion equations from boundary measurements
Archive for Rational Mechanics and Analysis, 247 (2023), no. 1, 6.
An inverse problem for the porous medium equation with a possibly absorption term
SIAM J. Math. Analysis, 55 (2023), 162–185.
Inverse boundary value problems for wave equations with quadratic nonlinearities
J. Differential Equations, 309 (2022), 558–607
Single pixel X-ray transform and related inverse problems
SIAM J. Imag. Sciences, 15 (2022), 1894–1909.
Inverse Problems for Einstein-Scalar Field Equations
Duke Math. J., 171 (2022), 3215–3282.
On the scientific work of Victor Isakov
Inverse Problems and Imaging, 16 (2022), 1429–1445.
An inverse boundary value problem for a semilinear wave equation on Lorentzian manifolds
International Math. Research Notices (IMRN), 17 (2022), 13181–13211.
The Higher Order Fractional Calderón Problem for Linear Local Operators: Uniqueness
Advances in Math, 399 (2022), 108246
Recovery of piecewise smooth density and Lamé parameters from high-frequency exterior Cauchy data
SIAM J. Imaging Sciences, 15 (2022), 1910–1943.
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.
Inverse Scattering for Critical Semilinear Wave Equations
Pure and Applied Analysis, 4 (2022), 191–223.
Nonlinear ultrasound imaging modeled by a Westervelt equation
SIAM J. Appl. Math, 82 (2022), 408-426.
On an Inverse Boundary Value Problem For A Nonlinear Elastic Wave Equation
Journal des Mathematiques Pures et Appliquees, 153 (2021), 114-136.
Travel Time Tomography in Stationary Spacetimes
Journal of Geometric Analysis, 31 (2021), 9573 - 9596.
The transmission problem in linear isotropic elasticity
Pure and Applied Analysis, 3 (2021), 109-161.
Local and global boundary rigidity and the geodesic X-ray transform in the normal gauge
Annals of Math., 194 (2021), 1-95.
Reconstruction of the Collision Term in the Nonlinear Boltzmann Equation
SIAM J. Math Analysis, 53, (2021), 1049 - 1069.
Optimality of increasing stability for an inverse boundary value problem
SIAM J. Math. Anal..bf 53 (2021), 7062–7080.
Reconstruction in the Calderón problem on conformally transversally anisotropic manifolds
J. Functional Analysis, 281 (2021), 109191.
Generic uniqueness and stability for mixed ray transforms
Transaction of the AMS, 374 (2021), 6085-6144.
Recovery of discontinuous Lamé parameters from local dynamic boundary data
Comm. in PDE, 46(2021), 680-715.
Inverse Problem for Fractional-Laplacian with Lower Order Non-local Perturbations
Trans. Amer. Math. Soc., 374 (2021), 3053-3075.
Determination of space-time structures from gravitational perturbations
Comm. Pure and Appl. Math., 73 (2020), 1315–1367
Convolutional neural networks in phase space and inverse problems
SIAM J. Appl. Math., 80(6) (2020), 2560–2585. (26 pages)
The Calderón problem for quasilinear elliptic equations
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 37 (2020), 1143-1166
The Light Ray transform on Lorentzian manifolds
Commun. Math. Phys. 377 (2020), 1349–1379.
Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities
Mathematics Research Letters, 27 (2020), 1801-1824.
A remark on partial data inverse problems for semilinear elliptic equations
Proc. Amer. Math. Soc. 148 (2020), 681-685
The Calderón problem for the fractional Schrödinger equation
Anal. PDE 13 (2020), 455–475.
Uniqueness and reconstruction for the fractional Calderón problem with a single measurement
Journal of Functional Analysis 279 (2020), 108505.
Nonlinear interaction of waves in elastodynamics and an inverse problem
Mathematische Annalen volume, 376 (2020), pages765–795
Recovery of material parameters in transversely isotropic media
Arch Rational Mech Anal, 235 (2020), 141–165
Lens rigidity for a particle in a Yang-Mills field
Comm. Math. Phys. 366 (2019), 681–707.
Inverse problems for the stationary transport equation in the diffusion scaling
SIAM J. Appl. Math., 79 (2019), 2340–2358.
Inverse Problems in Spacetime II: Reconstruction of a Lorentzian Manifold From Light Observation Sets
International Math. Research Notices (IMRN), 22 (2019), 6949–6987
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.
Reconstruction of Lorentzian manifolds from boundary light observation sets
International Math. Research Notices (IMRN), 22 (2019), 6949–6987.
X-ray transform and boundary rigidity for asymptotically hyperbolic manifolds
Annals of the Fourier Institute, Tome 69 No. 7 (2019), 2857-2919.
On an inverse boundary problem arising in brain imaging
J. Differential Equations, 267 (2019), 2471–2502.
Inverting the local geodesic ray transform of higher rank tensors
Inverse Problems, 35 (2019), 115009.
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.
Reconstruction of piecewise smooth wave speeds using multiple scattering
Trans. Amer. Math. Soc., 372 (2019), 1213-1235
Scattering Control for the Wave Equation with Unknown Wave Speed
Archive for Rational Mechanics and Analysis, 231(2019), 409-464.
Numerical inversion of 3D geodesic X-ray transform arising from traveltime tomography
SIAM J. Imaging Sci., 12(3) (2019), 1296–1323.
Inverting the local geodesic X-ray transform on tensors
Journal D’Analyse Math., 136 (2018), 151–208.
Inverse problems for magnetic Schrödinger operators in transversally anisotropic geometries
Comm. Math. Phys., 361 (2018), 525–582.
Inverse problems for advection diffusion equations in admissible geometries
Comm in PDE, 43 (2018), 585–615.
Propagation and recovery of singularities in the inverse conductivity problem
Analysis and PDE, 11(2018), 1901-1943
Tensor tomography in periodic slabs
Journal of Functional Analysis 275 (2018), no. 2, 288–299.
Inverse problems for Lorentzian manifolds and non-linear hyperbolic equations
Invent. Math. 212 (2018), no. 3, 781–857.
Inverse problems for semilinear wave equations on Lorentzian manifolds
Comm. Math. Physics. 360 (2018), no. 2, 555–609.
On the microlocal analysis of the geodesic X-ray transform with conjugate points
Journal of Differential Geometry 108 (2018), no. 3, 459–494.
On the inverse problem of finding cosmic strings and other topological defects
Comm. Math. Physics. 357 (2018), no. 2, 569–595.
Inversion formulas and range characterizations for the attenuated geodesic ray transform
Journal de Mathematiques Pures et Appliquees. (9) 111 (2018), 161–190.
Superdimensional Metamaterial Resonators from sub-Riemannian geometry
SIAM J. Appl. Math. 78 (2018), no. 1, 437–456.
Local recovery of the compressional and shear speeds from the hyperbolic DN map
Inverse Problems 34 (2018), no. 1, 014003.
Bounds on eigenfunctions of semiclassical operators with double characteristics
Asymptot. Anal. 106 (2018), no. 1, 25–46.
Quantitative analysis of metal artifacts in X-ray tomography
SIAM J. Math. Anal., 30 (2018), 4914-4936.
Reducing Streaking Artifacts in Quantitative Susceptibility Mapping
SIAM J.Imaging Science. 10 (2017), no. 4, 1921–1934.
An inverse problem from condense matter physics
Inverse Problems 33 (2017), no. 11, 115011
On regularized full- and partial-cloaks in acoustic scattering
Comm. PDE. 42(2017), 821-851.
Full and Partial Cloaking in Electromagnetic Scattering
Arch. Ration. Mech. Anal. 223 (2017), 265–299.
Absolute Continuity of the Periodic Schrödinger Operator in Transversal Geometry
J. Eur. Math. Soc. (JEMS) 19 (2017), 531–550.
The Inverse Problem for the Local Geodesic X-ray Transform.
Inventiones Mathematicae 205 (2016) 83–120
Local Analytic Regularity for the Linearized Calderon Problem
Analysis & PDE, 9 (2016), 515-544.
Boundary Rigidity with Partial Data
Journal of the AMS 29 (2016), 299–332.
On the stable recovery of a metric from the hyperbolic DN map with incomplete data
Inverse Probl. Imaging 10 (2016), 1141–1147.
The geodesic X-ray transform with matrix weights
American Journal of Mathematics, 141(6) (2016)
Inverse Boundary Problems for Polyharmonic Operators with Unbounded Potentials
J. Spectral Theory, 6 (2016), 145-183.
The Calderon problem with partial data for conductivities with 3/2 derivatives
Comm. Math. Phys. 348 (2016), 185–219.
The X-ray transform for connections in negative curvature
Comm. Math. Phys. 343 (2016), 83–127.
Reconstruction of a fully anisotropic elasticity tensor from knowledge of displacement fields
SIAM J. Appl. Math. 75 (2015), 2214–2231
Difraction by conormal singularities
Annales Scientifiques de l'Ecole Normale Superieure, 48 (2015), 351--408.
The Neumann-to-Dirichlet map in two dimensions.
Adv. Math. 281 (2015), 578–593.
On Lp Resolvent Estimates for Elliptic Operators on Compact Manifolds
Comm. PDE, 40 (2015), 438-474.
Inverse Boundary Value Problem for the Stokes and the Navier-Stokes Equations in the Plane
Arch. Ration. Mech. Anal. 215 (2015), 811-829
Regularized Transformation-Optics Cloaking for Helmholtz Equation: From Partial Cloak to Full Cloak.
Comm. Math. Phys., 335 (2015), 671--712
Determining both sound speed and internal source in thermo- and photo-acoustic tomography
Inverse Problems 31 (2015), 105005.
Regularized Transformation-Optics Cloaking in Acoustic and Electromagnetic Scattering
Inverse Problems and Imaging, Société mathématique de France, Panoramas et Syntheses, 44, (2015), 111-136.
The Geodesic Ray Transform on Riemannian Surfaces with Conjugate Points
Comm. in Mathematical Physics, 337, 1491--1513 (2015)
Invariant Distributions, Beurling Transform and Tensor Tomography in Higher Dimensions
Math. Ann. 363 (2015), 305–362.
On the Range of the Attenuated Ray Transform for Unitary Connections.
Int. Math. Res. Not. IMRN (2015), 873–897.
An Inverse Kinematic Problem with Internal Sources
Inverse Problems 31 055006 (2015)
The Point Source Inverse Back-Scattering Problem
Contemporary Math., 644 (2015), 279-289.
Inverse Electromagnetic Problems.
Encyclopedia of Applied and Computational Mathematics (2015) 716-725, Springer-Verlag, edited by B. Enquist.
Increasing Stability of the Inverse Boundary Value Problem for the Schroedinger Equation`.
Contemp. Math. 615 (2014), 131-141.
Determining a magnetic Schr\"odinger operator with a bounded magnetic potential from boundary measurements
Comm. Math. Phys., 327 (2014), 993-1009.
Inverse Boundary value Problems for the Perturbed Polyharmonic Operator
Transactions AMS, 366 (2014), 95-112.
Photoaocustic and Thermoacoustic Tomography with an Uncertain Wave Speed
Math. Research letters 21 (2014) 1199-1214
Spectral Rigidity and Invariant Distributions on Anosov Manifolds.
J. Differential Geom. 98 (2014), 147–181.
Tensor Tomography in Two Dimensions:Progress and Challenges.
. Chinese Annals of Math. Ser. B, Ser. B, 35 (2014), 399-427.
Uniqueness in the Backscattering Problem for Angularly Controlled Potentials
Inverse Problems, 30 (2014) 065005
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).
Inverse boundary problems for systems in two dimensions
Annales Intitut Henri Poincar\'e, 14 (2013), 1551-1571.
Reconstruction of coefficients in scalar second order elliptic equations from knowledge of their solutions.
Comm. on Pure and Applied Math., 66 (2013), 1692-1652.
Multi-scale discrete approximations of Fourier integral operators.
SIAM Multiscale Modeling and Simulation, 11 (2013), 566-585. .
Increasing Stability in an Inverse Problem for the Acoustic Equation.
Inverse Problems, 29 (2013), 229-247.
Tensor Tomography on Simple Surfaces.
Inventiones Math., 193 (2013), 229-247.
Is a Curve Flight Path in SAR Better than a Straight One?
SIAM J. Appl. Math., 73 (2013), 1596-1612.
Recovery of a Source or a Speed with One Measurement and Applications
Transactions AMS., 365 (2013), 5737-5758.
Instability for the Linearized Problem in Multiwave Tomography of Recovery Both the Source and the Speed.
Inverse Problems and Imaging, 7 (2013), 1367-1377.
Reconstructions for some coupled physics problems.
Applied Mathematics Letters, 25 (2012), 1030-1033.
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.
Schroedinger's Hat: Approximate Electromagnetic, Acoustic and Quantum Amplifiers Via Transformation Optics.
Proceedings National Academy of Sciences (PNAS), 109 (2012), 10169-10174.
On Reconstruction of Lam\'e Parameters from Partial Cauchy Data in Three Dimensions.
Inverse Problems, 28 (2012), 125002.
Partial Cauchy Data for General Second Order Elliptic Operators in Two Dimensions.
Publ. Research Insti. Math. Sci, 48 (2012), 971-1055.
Determining a First Order Perturbation of the Biharmonic Operator by Partial Boundary Measurements
Journal Functional Analysis, 262 (2012), 1781-1801.
Inverse Problems with Partial Data for a Magnetic Schroendinger Operator in an Infinite Slab or Bounded Domain
Comm. Math. Phys., 312 (2012), 87-126.
The Attenuated Ray Transform for Connections and Higgs Fields.
Geometric and Functional Analysis (GAFA), 22 (2012), 1460-1480.
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).
Polarization Invariant Directional Cloaking by Transformation Optics.
Progress In Electromagnetics Research, Vol. 118 (2011), 415-423. Comm. Math. Phys., 312 (2012), 87-126.
The Attenuated Ray Transform for Connections and Higgs Fields.
Geometric and Functional Analysis (GAFA), 22 (2012), 1460-1480.
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).
Polarization Invariant Directional Cloaking by Transformation Optics.
Progress In Electromagnetics Research, Vol. 118 (2011), 415-423.
Cloaking a Sensor for Three Dimensional Maxwell's Equations: A Transformation Optics Approach.
Optics Express, 19 (2011), 20518-20530.
Inverse Boundary Problem with Cauchy data on Disjoint Sets.
Inverse Problems, 27 (2011), 085007.
An Efficient Neumann-series Based Algorithm for the Thermoacoustic and Photoacoustic Tomography with Variable Sound Speed
SIAM J. Imaging Sciences, 4 (2011), 850-883.
An Adaptive Method in Phase Space with Application to Reflection Travel Time Tomography
Inverse Problems, 27 (2011) 115002.
Reconstruction from Boundary Measurements for Admissible Manifolds
Inverse Problems and Imaging, 5 (2011), 859 - 877.
Cloaking a Sensor via Transformation Optics
Physical Review E, 83 (2011), 016603.
Partial Cauchy Data for General Second Order Elliptic Operators in Two Dimensions.
Publ. Research Insti. Math. Sci, 48 (2012), 971-1055.
On Determination of Second Order Elliptic Operators from Partial Cauchy Data.
Proceedings National Academy of Sciences, 108 (2011), 467-472.
Quantitative Thermoacoustics and Related Topics.
Inverse Problems, 27 (2011), 055007.
Thermoacoustic Tomography Arising in Brain Imaging
Inverse Problems, 27 (2011), 045004.
The Elastic Wave Equation of Limited Smoothness
Comm. PDE., 36 (2011), 1683-1693.
Asymptotic Behavior of Solutions of the Stationary Navier Stokes Equation in Exterior Domains
Indiana Math. J., 60 (2011), 2093-2106.
The Attenuated Ray Transform on Simple Surfaces
J. Diff. Geometry, 88 (2011), 161-187.
Wave Imaging
Handbook of Mathematical Methods in Imaging, Springer-Verlag, O. Scherzer (Ed.), 2011.
Quantitative Unique continuation for the Lame System with Less Regular Coefficients
Methods and Applications of Analysis, 18 (2011), 85-92.
Inverse Problems for Differential Forms on Riemannian Manifolds with Boundary
Comm. PDE, 36 (2011), 1475-1509.
The Geodesic X-Ray Transform with Fold Caustics
Anal. and PDE., 5 (2012), 219-260.
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.
Approximate Acoustic and Quantum Cloaking
Journal Spectral Theory, 1 (2011), 27-80.
Inverse Problems for the Anisotropic Maxwells Equations
Duke Math. J., 157 (2011), 369-419.
Reconstruction of Penetrable Obstacles in Acoustics
SIAM J. Math. Anal., 43 (2011), 189-211.
Inverse Diffusion Theory of Photoacoustics.
Inverse Problems, 26(2010), 085010.
Reconstructing the Metric and Magnetic Field from the Scattering Relation
Inverse Problems and Imaging, 4(2010), 397-409.
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.
Inverse Problems on a Slab
Inverse Problems and Imaging, 4(2010), 449-462.
Inverse Scattering for the Magnetic Schroedinger Equation
J. Funct. Anal. 259, (2010), 1771-1798.
On the Linearized Local Calderon Problem,
Math Research Letters, 16(2009), 955-970.
Limiting Carleman Weights and Anisotropic Inverse Problems.
Inventiones Math, 178(2009), 119-171.
Seismic Imaging with the Generalized Radon Transform: A Curvelet Transform Perspective
Inverse Problems 25 (2009) 025005
Cloaking Devices, Electromagnetic Wormholes and Transformation Optics
SIAM Review 51 (2009), 3-33.
Invisibility and Inverse Problems
Bulletin AMS 46 (2009), 55-97.
Depth Dependent Stability estimates in Electrical Impedance Tomography
Inverse Problems 25 (2009), 075001.
Thermoacoustic Tomography with Variable Sound Speed
Inverse Problems, 25 (2009), 075011.
Linearizing Non-linear Inverse Problems and its Applications to Inverse Backscattering
Journal Functional Analysis 256 (2009), 2842-2866.
Local Lens Rigidity with Incomplete Data for a Class of Non-Simple Riemannian Manifolds
Journal Diff. Geometry 82 (2009), 383-409.
Calderon's Problem and Electrical Impedance Tomography.
Inverse Problems, 25th Anniversary Volume, 25(2009), 123011 (39pp.)
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.
Unique Continuation Property with General Residual Stress
Inverse Problems and Imaging 3 (2009), 309-317.
Reconstruction of Inclusions in an Elastic Body
Journal de Mathematiques Pures et Appliquees (2009), 569-582.
A Multi-Scale Approach to Hyperbolic Equations with Limited Smoothness
Comm. P.D.E., 33 (2008), 988-1017
A Phase-space Formulation for Elastic-wave Traveltime Tomography
Journal of Physics: Conference Series 124 (2008), 012018.
Approximate Quantum Cloaking and Almost Trapped States
Physical Review Letters 101 (2008), 220404.
Isotropic Transformation Optics: Approximate Acoustic and Quantum Cloaking
New Journal of Physics 10 (2008), 115024-115051.
Inverse Problems, Invisibility, and Artificial Wormholes
Journal of Physics: Conference Series 124 (2008), 012005.
Electromagnetic Wormholes via Handlebody Constructions
Communications in Mathematical Physics, 281 (2008), 369-385
Generalized Backscattering and the Lax-Phillips Transform
Serdica Math. J. 34 (2008), 1026-1044
An Inverse Problem in Optical Molecular Imaging
Analysis and PDE 1 (2008), 115-126.
The X-Ray Transform for a Generic Family of Curves and Weights
J. Geom. Anal. 18(1)(2008), 81-97
Integral Geometry of Tensor fields on a Class of Non-Simple Riemannian Manifolds
American J. of Math., 130 (2008), 239-268.
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.
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.
Complex Geometrical Optics Solutions and Reconstruction of Discontinuities
SIAM J. Appl. Math., 68 (2008), 1026-1044.
A New Phase Space Method for Recovering Index of Refraction from Travel Times
Inverse Problems 23 (2007), no. 1, 309--329.
The Boundary Rigidity Problem in the Presence of a Magnetic Field
Adv. Math. 216(2)(2007), 535-609.
Determining the Magnetic Schr\"odinger Operator from Partial Cauchy Data.
Comm. Math. Phys. 271 (2007), no. 2, 467--488.
Effectiveness and Improvement of Cylindrical Cloaking with the SHS Lining
Optics Express, Vol. 15, Issue 20, pp. 12717-12734 (2007)
Electromagnetic Wormholes and Virtual Magnetic Monopoles from Metamaterials
Physical Review Letters, 99, no. 18, 183901 (2007)
Full Wave Invisibility of Active Devices at all Frequencies
Communications in Mathematical Physics, 275, no. 3 (2007), 749-789.
Reconstruction of Obstacles Immersed in an Incompressible Fluid
Inverse Probl. Imaging 1 (2007), no. 1, 63--76.
Probing for electrical inclusions with complex spherical waves.
Communications on Pure and Applied Mathematics 60 (2007), pp. 1415-1442
The Calder\'on Problem with Partial Data.
Ann. of Math. (2) 165 (2007), no. 2, 567--591.
Parametrices for systems with multiplicity
Wave Motion 44 (2007), no. 4, 231--247.
Complex Geometrical Optics Solutions for Anisotropic Equations and Applications
J. Inv. Ill-Posed Problems 16 (2007), 791-804.
Complex spherical waves for the elasticity system and probing of inclusions
SIAM J. Math. Anal. 38 (2007), no. 6, 1967--1980.
Reconstructing Discontinuities in Systems
Journal of Physics: Conference Series (2007), 012024.
Characterization and source-receiver continuation of seismic reflection data
Comm. Math. Physics, 263(2006), 1-19.
Oscillating Decaying Solutions for Elliptic Systems,
Contemporary Math., 408(2006), 219-230. .
The Scattering Relation and the Dirichlet-to-Neumann Map
Contemporary Math, 412(2006), 249-262.
Oscillating Decaying Solutions, Runge Approximation and its Applications to Inverse Problems
Journal de Mathematiques Pures et Appliquees, 85(2005), 21-54.
Two Dimensional Compact Simple Riemannian manifolds are Boundary Distance Rigid
Annals of Math., 161(2005), 1089-1106.
Reconstruction of Cracks in an Inhomogeneous Anisotropic Medium Using Point Sources
Advances in Appl. Math., 34 (2005),591--615.
Regularity of Ghosts in Tensor Tomography
Journal of Geometric Analysis, 15 (2005), 499-542.
`
Boundary Rigidity and Stability for Generic Simple Metrics,
Journal Amer. Math. Soc. 18(2005), 975-1003.
Stable Determination of Generic Simple Metrics from the Hyperbolic Dirichlet-to-Neumann Map
International Math. Research Notices, 17(2005), 1047-1061.