Online Papers

• Scalar curvature and Geometrization Conjectures for 3-manifolds,
  Comparison Geometry, M.S.R.I. Publ.,vol.30, (1997), 49-82.
  (PostScript, or PDF).
• Scalar curvature, metric degenerations and the static vacuum Einstein equations on 3-manifolds, I,
  Geom. & Funct. Analysis., vol.9:5, (1999), 855-967
  (DVI, or PostScript, or PDF)
• Scalar curvature, metric degenerations and the static vacuum Einstein equations on 3-manifolds, II,
  Geom. & Funct. Analysis, vol. 11, (2001), 273-381.
  (DVI, or PostScript, or PDF)
• Scalar curvature and the existence of geometric structures on 3-manifolds, I,
  Journal fur die Reine und Angewandte Math., vol. 553, (2002), 125-182.
  (DVI, or PostScript, or PDF)
• Scalar curvature and the existence of geometric structures on 3-manifolds, II,
  Journal fur die Reine und Angewandte Math., vol 563, (2003), 115-195.
  (DVI, or PostScript, or PDF)
• Extrema of curvature functionals on the space of metrics on 3-manifolds,
  Calc. Var. and P.D.E., vol. 5, (1997), 199-269.
• Extrema of curvature functionals on the space of metrics on 3-manifolds, II,
  Calc. Var. and P.D.E, vol. 12, (2001), 1-58.
  (DVI, or Postscript, or PDF).
• Geometrization of 3-manifolds via the Ricci flow,
  Notices of the A.M.S., vol. 51, (Feb. 2004), 184-193.
  (PDF)
• Remarks on Perelman's papers,
  (July, 03)
  (DVI, or Postscript, or PDF).
• Singularities of the Ricci flow,
  (June 05, to appear in Encyclopedia of Mathematical Physics, Elsevier)
  (DVI, or Postscript, or PDF).

• On the structure of solutions to the static vacuum Einstein equations,
  Annales Henri Poincare, vol. 1, (2000), 995-1042.
  (DVI, PostScript, or PDF).
• On stationary vacuum solutions to the Einstein equations,
  Annales Henri Poincare, vol. 1, (2000), 977-994.
  (DVI, or PostScript, or PDF).
• Asymptotic behavior of static and stationary vacuum space-times,
  Proc. IX Marcel Grossmann Meeting, Rome, 2000, 989-990, World Scientific, (2003).
  (DVI, or PostScript, or PDF).
• On long-time evolution in general relativity and geometrization of 3-manifolds,
  Comm. Math. Phys, vol. 222, (2001), 533-567.
  (DVI, or PostScript, or PDF)
• Remarks on evolution of space-times in 3+1 and 4+1 dimensions,
  Classical and Quantum Gravity, vol. 18, (2001), 5199-5209.
  (DVI, or PostScript, or PDF)
• Cheeger-Gromov theory and applications to General Relativity,
  in: The Einstein Equations and the Large Scale Behavior of Gravitational Fields,
  (Cargese 2002), Ed. P.T. Chrusciel and H. Friedrich, Birkauser, Basel, (2004), 347-377.
  (DVI, or PostScript,or PDF).
• Regularity for Lorentz metrics under curvature bounds,
  Jour. Math. Physics, 44, (2003), 2994-3012.
  (DVI, or Postscript, or PDF)
• Nontrivial, static, geodesically complete, vacuum space-times with a negative cosmological constant,
  with P. Chrusciel and E. Delay.
  Jour. High Energy Physics, 10 (2002) 063, 1-27.
  (DVI, or Postscript, or PDF)
• Nontrivial, static, geodesically complete space-times with a negative cosmological constant, II: n > 4
  with P. Chrusciel and E. Delay, in:
  AdS/CFT Correspondence: Einstein Metrics and Their Conformal Boundaries,
  Ed. O. Biquard, Euro. Math. Soc. Zurich, (2005), 165-204.
  (DVI, or Postscript, or PDF)
• Asymptotics of future-complete cosmological space-times,
  Classical and Quantum Gravity, (Spacetime Safari Issue in Honor of Vince Moncrief), vol. 21 (2004), S11-S27.
  (DVI, or Postscript, or PDF)
• Existence and stability of even dimensional asymptotically de Sitter spaces
  Annales Henri Poincare, vol. 6, (2005), 801-820.
  (DVI, or Postscript, or PDF)
• Asymptotically simple solutions of the vacuum Einstein equations in even dimensions
  with P. Chrusciel.
  Comm. Math. Phys., vol. 260, (2005), 557-577.
  (DVI, or Postscript, or PDF)
• On the Bartnik extension problem for static vacuum Einstein metrics,
  with Marcus Khuri,
  Classical and Quantum Gravity, vol. 30, 125005, (2013)
  (PDF)
• On quasi-local Hamiltonians in General Relativity,
  Phys. Rev. D, vol. 82, (15 October 2010), 084044
  (DVI, or Postscript, or PDF)
• Local existence and uniqueness for exterior static vacuum Einstein metrics,
  Proc. Amer. Math. Soc., vol. 143, (2015), 3091-3096.
  (PDF)
• On the Bartnik conjecture for the static vacuum Einstein equations,
  Classical and Quantum Gravity, vol. 33:1, (2016), 015001
  (PDF)
• Embeddings, immersions and the Bartnik quasi-local mass conjectures,
  with J. Jauregui,
  Ann. Henri Poincare, vol. 20, (2019), 1651-1698
  (PDF)
• On the conformal method for the Einstein constraint equations,
  Adv. Theor. Math. Phys, Vol. 24:6, (2020), 1325-1374.
  (PDF)
• Recent progress and problems on the Bartnik quasi-local mass,
  Pure Appl. Math Quarterly, vol. 15, (2019), 851-873.
  (PDF)
• On the initial boundary value problem for the vacuum Einstein equations and geometric uniqueness,
  with Zhongshan An
  (preprint, May 2020, 42 pages)
  (PDF)
• The initial boundary value problem and quasi-local Hamiltonians in General Relativity,
  with Zhongshan An
  Class. Quantum Grav, vol. 38:15, (2021), 154001.
  (PDF)
• The Bartnik quasi-local mass conjectures,
  (preprint, August 2023, 32 pages).
  (PDF)

• L^2 curvature and volume renormalization of AHE metrics on 4-manifolds,
  Math. Research Letters, vol. 8, (2001), 171-188.
  (DVI, PostScript, or PDF)
• Boundary regularity, uniqueness and non-uniqueness for AH Einstein metrics on 4-manifolds,
  Adv. in Math., vol. 179, (2003), 205-249,
  (DVI, or PostScript, or PDF)
• On the structure of conformally compact Einstein metrics,
  Calc. Var. and PDE, vol. 39, (2010), 459-489.
  (DVI, or PostScript, or PDF)
• Dehn filling and Einstein metrics in higher dimensions,
  Jour. Diff. Geom, vol. 73, (2006), 219-261.
  (DVI, or PostScript, or PDF)
• Peaks in the Hartle-Hawking wave function from sums over topologies,
  with S. Carlip, J. Ratcliffe, S. Surya and S. Tschantz
  Classical and Quantum Gravity, vol. 21, (2004), 729-741.
  (DVI, or Postscript, or PDF)
• Geometric aspects of the AdS/CFT correspondence,
  in: AdS/CFT Correspondence: Einstein Metrics and Their Conformal Boundaries,
  Ed. O. Biquard, Euro. Math. Soc., Zurich, (2005), 1-31.
  (DVI, or Postscript, or PDF)
• On the structure of asymptotically de Sitter and anti-de Sitter spaces,
  Adv. Theor. Math. Physics, vol. 8, (2004), 861-893.
  (DVI, or Postscript, or PDF)
• Topics in conformally compact Einstein metrics,
  in: Perspectives in Riemannian Geometry, Ed. V. Apostolov, et. al,
  CRM Proceedings, vol. 40, Amer. Math. Soc. (2006), 1-26.
  (DVI, or Postscript, or PDF)
• Canonical metrics on 3-manifolds and 4-manifolds,
  Asian Journal of Math., vol. 10, (2006), 127-164.
  (DVI, or Postscript, or PDF)
• On the uniqueness and global dynamics of AdS spacetimes,
  Class. Quantum Grav., vol. 23, (2006), 6935-6953.
  (DVI, or Postscript, or PDF)
• Unique continuation results for Ricci curvature and applications,
  (with Marc Herzlich),
  Journal of Geometry and Physics, vol. 58, (2008), 179-207.
  (DVI, Postscript, or PDF)
• Erratum: Unique continuation results for Ricci curvature and applications,
  (with Marc Herzlich),
  Journal of Geometry and Physics, vol. 60, (2010), 1062-1067.
  (DVI, Postscript, or PDF)
• Einstein metrics with prescribed conformal infinity on 4-manifolds,
  Geometric and Functional Analysis, vol. 18, (2008), 305-366.
  (DVI, or PostScript, or PDF)
• On boundary value problems for Einstein metrics,
  Geometry & Topology, vol. 12, (2008), 2009-2045.
  (DVI, or Postscript, or PDF)
• Extension of symmetries on Einstein manifolds with boundary,
  Selecta Mathematica, vol. 16, (2010), 343-375.
  (PDF)
• A survey of Einstein metrics on 4-manifolds,
  in: Handbook of Geometric Analysis III, Ed. L. Ji,
  P. Li, R. Schoen, L. Simon, International Press, Boston, (2010), 1-30.
  (DVI, or Postscript, or PDF)
• Holographic Uniformization,
  with C. Beem, N. Bobev and L. Rastelli, (preprint, Sept. 2011, 52p).
  Commm. Math. Phys., vol. 318:2 (2013), 429-471.
  (PDF)
• On the local rigidity of Einstein manifolds with convex boundary,
  (preprint Oct 2012 - under reconstruction)
  
• Static vacuum Einstein metrics on bounded domains,
  Annales Henri Poincare, vol. 16, (2015), 2265-2302.
  (PDF)
• Alexandrov immersions, holonomy and minimal surfaces in S^3,
  (preprint, July 2014 - under reconstruction)
  

• Boundary regularity for the Ricci equation, geometric convergence and Gel'fand's inverse boundary problem,
  with A. Katsuda, Y. Kurylev, M. Lassas and M. Taylor.
  Inventiones Math, vol. 158, (2004), 261-321.
  (PostScript, or PDF)
• Metric tensor estimates, geometric convergence, and inverse boundary problems,
  with A. Katsuda, Y. Kurylev, M. Lassas and M. Taylor.
  Elec. Res. Annc. of A.M.S. vol. 9, (2003), 69-79.
  (PostScript, or PDF)
• On uniqueness and differentiability in the space of Yamabe metrics,
  Comm. Contemp. Math. vol. 7, (2005), 299-310.
  (DVI, or Postscript, or PDF).
• Orbifold compactness for spaces of Riemannian metrics and applications,
  Math. Annalen, vol. 331, (2005), 739-778.
  (DVI, or Postscript, or PDF).
• The compactification of a minimal submanifold in Euclidean space by the Gauss map,
  (old paper, 1984-86, IHES/Caltech Preprint, never published: Journal had the paper 30+ months, then editor said it was "lost", 31pp)
  (PDF); scan of original paper.
• Boundary value problems for metrics on 3-manifolds,
  in: Metric and Differential Geometry, in Honor of J. Cheeger, Eds. X. Dai and X. Rong,
  Birkhauser Verlag, Basel, (2012), 3-17.
  (DVI, or Postscript, or PDF).
• Conformal immersions of prescribed mean curvature in R^3,
  Nonlinear Analysis, vol. 114 (2015), 142-157.
  (DVI, or Postscript, or PDF).
• Elliptic regularization of the isometric immersion problem,
  Jour. Geom. Analysis, vol. 28, (2018), 2768-2779. (PDF)
• The Nirenberg problem of prescribed Gauss curvature on S^2,
  Comm. Math. Helv, vol. 96 (2021), 215-274. (PDF)