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.