Hubert Bray

Hubert Bray

Professor of Mathematics

Director of Undergraduate Studies in the Department of Mathematics

Office Location: 
189 Physics Bldg, Durham, NC 27710
Front Office Address: 
Box 90320, Durham, NC 27708-0320
Phone: 
(919) 757-8428

Overview

Professor Bray uses differential geometry to understand general relativity, and general relativity to motivate interesting problems in differential geometry. In 2001, he published his proof of the Riemannian Penrose Conjecture about the mass of black holes using geometric ideas related to minimal surfaces, scalar curvature, conformal geometry, geometric flows, and harmonic functions. He is also interested in the large-scale unexplained curvature of the universe, otherwise known as dark matter, which makes up most of the mass of galaxies. Professor Bray has proposed geometric explanations for dark matter which he calls "wave dark matter," which motivate very interesting questions about geometric partial differential equations.

Professor Bray has supervised 8 math Ph.D. graduates at Duke from 2006 to 2017. He is currently supervising one math Ph.D. student and one physics Ph.D. student. His most recent Ph.D. graduate, Henri Roesch, proved a Null Penrose Conjecture, open since 1973, as his thesis. While the physical motivation about the mass of black holes is the same as for the Riemannian Penrose Conjecture, the geometry involved is almost unrecognizably different, and may be viewed as a fundamental result about null geometry.

Education & Training

  • Ph.D., Stanford University 1997

  • B.A., Rice University 1992

Bray, H. L., and M. A. Khuri. “P. D. E. 'S which imply the penrose conjecture.” Asian Journal of Mathematics, vol. 15, no. 4, Jan. 2011, pp. 557–610. Scopus, doi:10.4310/AJM.2011.v15.n4.a5. Full Text

Bray, H., et al. “Area-Minimizing Projective Planes in 3-Manifolds.” Communications on Pure and Applied Mathematics, vol. 63, no. 9, Sept. 2010, pp. 1237–47. Scopus, doi:10.1002/cpa.20319. Full Text

Bray, H. L., and M. A. Khuri. “A jang equation approach to the penrose inequality.” Discrete and Continuous Dynamical Systems, vol. 27, no. 2, June 2010, pp. 741–66. Scopus, doi:10.3934/dcds.2010.27.741. Full Text

Bray, H., et al. “Rigidity of area-minimizing two-spheres in three-manifolds.” Communications in Analysis and Geometry, vol. 18, no. 4, Jan. 2010, pp. 821–30. Scopus, doi:10.4310/CAG.2010.v18.n4.a6. Full Text

Bray, H. L., and D. A. Lee. “On the Riemannian Penrose inequality in dimensions less than eight.” Duke Mathematical Journal, vol. 148, no. 1, May 2009, pp. 81–106. Scopus, doi:10.1215/00127094-2009-020. Full Text

Bray, H., and P. Miao. “On the capacity of surfaces in manifolds with nonnegative scalar curvature.” Inventiones Mathematicae, vol. 172, no. 3, June 2008, pp. 459–75. Scopus, doi:10.1007/s00222-007-0102-x. Full Text

Bray, H., et al. “Generalized inverse mean curvature flows in spacetime.” Communications in Mathematical Physics, vol. 272, no. 1, May 2007, pp. 119–38. Scopus, doi:10.1007/s00220-007-0203-9. Full Text

Bray, H. L., and A. Neves. “Classification of Prime 3-Manifolds with Yamabe Invariant Greater than RP^3.” Annals of Mathematics, vol. 159, no. 1, Jan. 2004, pp. 407–24.

Bray, H., and F. Finster. “Curvature estimates and the Positive Mass Theorem.” Communications in Analysis and Geometry, vol. 10, no. 2, Jan. 2002, pp. 291–306. Scopus, doi:10.4310/CAG.2002.v10.n2.a3. Full Text

Pages

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