Hubert L. Bray, Professor

Professor Bray studies differential geometry and partial differential equations, often with applications to general relativity.

Contact Info:

Office Location:	189 Physics
Office Phone:	(919) 757-8428 (mobile), (919) 660-2818 (office)
Email Address:

Teaching (Spring 2010):

• MATH 105.01, VECTOR CALCULUS Synopsis

  Physics 235, TuTh 10:05 AM-11:20 AM

• MATH 268.01, DIFFERENTIAL GEOMETRY Synopsis

  Physics 205, TuTh 08:30 AM-09:45 AM

Education:

PhD

Stanford University

1997

Specialties:

Geometry
Mathematical Physics

Research Interests: Geometric Analysis, General Relativity

Current Ph.D. Students   (Former Students)

• Jeff Jauregui  
• M. George Lam  
• Graham H. Cox  
• Alan R. Parry  

Representative Publications   (More Publications)

1. H.L. Bray, The Penrose Inequality in General Relativity and Volume Comparison Theorems Involving Scalar Curvature (1997) (thesis, Stanford University.) [arXiv:0902.3241v1]
2. H. L. Bray, Proof of the Riemannian Penrose Inequality Using the Positive Mass Theorem, Journal of Differential Geometry, vol. 59 no. 2 (2001), pp. 177--267 [arXiv:math/9911173v1]
3. H. L. Bray and F. Finster, Curvature Estimates and the Positive Mass Theorem, Communications in Analysis and Geometry, vol. 10 no. 2 (2002), pp. 291--306 [arXiv:math/9906047v3]
4. H.L. Bray and A. Neves, Classification of Prime 3-Manifolds with Yamabe Invariant Greater than RP^3, Annals of Mathematics, vol. 159 no. 1 (2004), pp. 407--424
5. H.L. Bray, A Family of Quasi-local Mass Functionals with Monotone Flows, in Proceedings of the 14th International Congress on Mathematical Physics, Lisbon, Portugal, 2003, edited by Jean-Claude Zambrini (2003)
6. H.L. Bray, P. Miao, On the Capacity of Surfaces in Manifolds with Nonnegative Scalar Curvature, Inventiones Mathematicae, vol. 172 no. 3 (June, 2008) [arXiv:0707.3337v1]
7. H.L. Bray, D.A. Lee, On the Riemannian Penrose Inequality in Dimension Less Than Eight, Duke Mathematical Journal, vol. 148 no. 1 (2009), pp. 81-106 [arXiv:0705.1128v1]
8. H.L. Bray and J.L. Jauregui, A Geometric Theory of Zero Area Singularities in General Relativity (Submitted, 2009) [arXiv:0909.0522v1]
9. H.L. Bray and M.A. Khuri, P.D.E.'s Which Imply the Penrose Conjecture (Submitted, 2009) [arXiv:0905.2622v1]
10. H.L. Bray, S. Brendle, M. Eichmair, A. Neves, Area-Minimizing Projective Planes in 3-Manifolds (Submitted, 2009) [arXiv:0909.1665v1]

Recent Grant Support

• Geometric Analysis Applied to General Relativity, National Science Foundation, DMS-0706794, 2007/07-2010/06.      
• Extension to June 2008 of NSF Grant, National Science Foundation, DMS-0533551 (DMS-0206483 before transfered to Duke), 2002/09-2007/09.