Research Interests

• Mathematical general relativity: a sampler.
  with Piotr T. Chruściel and Gregory Galloway
  Institut Mittag-Leffler REPORT No. 3, 2008/2009, fall. 84 pages.
  Preprint
  
  
• 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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