Research Interests
You can link to several items related to my research.
Research Papers (with links to preprints at the arXiv e-Print
archive or electronic versions of published papers)
- Causal geodesic incompleteness of spacetimes arising from IMP gluing
with Madeleine Burkhart
arXiv:1907.00295
- Null geodesic incompleteness of spacetimes with no CMC Cauchy surfaces
with Madeleine Burkhart and Martin Lesourd
arXiv:1902.07411
To appear, Pure and Applied Mathematics Quarterly
- On the geometry and topology of initial data sets with
horizons
with Lars Andersson, Mattias Dahl and Gregory Galloway
arXiv:1508.01896
Article in
Asian Journal of Mathematics online
Asian J. Math. Vol. 22, No. 5, pp. 863-882, October 2018
- Topological Censorship from the initial data point of view
with Michael Eichmair and Gregory Galloway
arXiv:1204.0278
Article in
Journal of Differential Geometry online
J. Differential Geom. 95 (2013), no. 3, 389-405.
- A refined result on sign changing solutions for a critical elliptic problem
with Yuxin Ge, Monica Musso, and Angela Pistoia
Commun. Pure and Applied Analysis 12 (2013) Issue 1, 125-155.
- Scalar Curvature and the Einstein Constraint Equations
with Justin Corvino
arXiv:1102.5050
Surveys in Geometric Analysis and Relativity, ALM 20 International Press (2011) 145-188.
- Mathematical general relativity: a sampler.
with Piotr T. Chruściel and Gregory Galloway
arXiv:1004.1016
Article in Bulletin of the AMS online.
Bulletin (New Series) of the American Mathematical Society 47 (2010), Number 4, 567-638.
- Singular Yamabe metrics and initial data with exactly
Kottler-Schwarzschild-de Sitter ends II. Generic metrics.
with Piotr T. Chruściel and Frank Pacard
arXiv:0803.1817
Article in
Mathematical Research Letters online
Mathematical Research Letters 16 (2009) 1, 157-164.
- Singular Yamabe metrics and initial data with exactly
Kottler-Schwarzschild-de Sitter ends
with Piotr T. Chruściel
gr-qc/0710.3365
Article in Annales Henri Poincaré online
Annales Henri Poincaré 9 (2008) 4, 639-654
- A variational analysis of Einstein-scalar field
Lichnerowicz equations on compact Riemannian manifolds
with Emmanuel Hebey and Frank Pacard
gr-qc/0702031
Article in Communications in Mathematical Physics online
Comm. Math. Phys. 278 (2008) 117--132
- Applications of theorems of Jean Leray to the Einstein-scalar field
equations
with Yvonne Choquet-Bruhat and James Isenberg
gr-qc/0611009
Isaac Newton Institute Preprint No. NI06050-GMX, 21 pages.
Article in Journal of Fixed Point Theory and Applications online
J. fixed point theory appl. 1 (2007) 31--46.
- The constraint equations for the Einstein-scalar field system on
compact manifolds
with Yvonne Choquet-Bruhat and James Isenberg
gr-qc/0610045
Isaac Newton Institute Preprint No. NI06045-GMX, 22 pages.
Article in Classical and Quantum Gravity online
Class. Quantum Grav. 24 (2007) 809--828
- A brief review of initial data engineering
with Piotr T. Chruściel and James Isenberg
Gravitation and Astrophysics, On
the Occasion of the 90th Year of General Relativity
Proceedings of the VII Asia-Pacific International Conference
National Central University, Taiwan 23 - 26 November 2005.
(ed. J. M. Nester, C. M. Chen and J. P. Hsu), World Scientific (2006)
PDF format preprint
- The Einstein-scalar field constraints on asymptotically
Euclidean manifolds
with Yvonne Choquet-Bruhat and James Isenberg
gr-qc/0506101
Article in Chinese Annals of Mathematics online
Chin. Ann. Math., 27 ser. B, (2006) 31--52.
- A gluing construction for non-vacuum solutions of the
Einstein constraint equations
with David Maxwell and James Isenberg
gr-qc/0501083
Article in Advances in Theoretical and Mathematical Physics online
Adv. Theor. Math. Physics 9 (2006) 129--172
- Gluing Initial Data Sets for General Relativity
with Piotr T. Chruściel and James Isenberg
gr-qc/0409047
Article in Physical Review Letters online
Phys. Rev. Lett. 93, 081101 (2004)
- Initial data engineering
with Piotr T. Chruściel and James Isenberg
gr-qc/0403066
Article in Communications in Mathematical Physics online
Comm. Math. Phys. 257 (2005) 1, 29--42
- On the topology of vacuum spacetimes
gr-qc/0206034
Article in Annales Henri Poincaré online
with James Isenberg and Rafe Mazzeo
Annales Henri Poincaré 4 (2003) 2, 369-383
- The conformal theory of Alexandrov embedded constant mean curvature
surfaces in $R^3$
math.DG/0110099
with Rafe Mazzeo and Frank Pacard
Global Theory of Minimal Surfaces,
David Hoffman, ed., AMS/Clay Mathematics Proceedings, Vol. 2 (2005).
- Gluing and wormholes for the Einstein constraint equations
gr-qc/0109045
Article in Communications in Mathematical Physics online
with James Isenberg and Rafe Mazzeo
Comm. Math. Phys. 231 (2002) 3, 529-568
- Connected sums of constant mean curvature surfaces in Euclidean
3 space
Article in
Crelles Journal online (PDF format)
with Rafe Mazzeo and Frank Pacard
J. Reine Angew. Math. 536 (2001), 115--165.
- Gluing and moduli for noncompact geometric problems
dg-ga/9601008
with Rafe Mazzeo
Geometric Theory of Singular Phenomena in
Partial Differential Equations
Symposia Mathematica, Vol. XXXVIII
Cambridge University Press, July 1998
- The Moduli space of complete embedded constant mean curvature
surfaces
with Rob Kusner and Rafe Mazzeo
Geom. Funct. Anal. 6, no. 1, (1996) 120--137.
- Moduli spaces of singular Yamabe metrics
Article in JAMS online (Multiple formats)
with Rafe Mazzeo and Karen Uhlenbeck
J. Amer. Math. Soc. 9, no. 2, (1996) 303--344.
- Connected sum constructions for constant scalar curvature
metrics
with Rafe Mazzeo and Karen Uhlenbeck
Topol. Methods Nonlinear Anal. 6, no. 2, (1995) 207--233.
- Compactness results for complete metrics of constant positive
scalar curvature on subdomains of $S^{n}$
Article in IUMJ online
Indiana Univ. Math. J. 42 no. 4 (1993) 1441 -- 1456.
- Nonuniqueness and high energy solutions for a conformally invariant
scalar equation
Comm. Anal. and Geom. 1 (1993) 347 -- 414.
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