# Hubert Bray

### **Professor of Mathematics**

Director of Undergraduate Studies in the Department of Mathematics

Professor in the Department of Physics (Secondary)

Professor of Physics (Secondary)

Director of Undergraduate Studies in the Department of Mathematics

Professor in the Department of Physics (Secondary)

Professor of Physics (Secondary)

### 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.

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.
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Bray, H. L., and K. Iga. “Superharmonic Functions in R^n and the Penrose Inequality in General Relativity.” *Communications in Analysis and Geometry*, vol. 10, no. 5, 2002, pp. 999–1016.

Bray, H. L. “Black Holes, Geometric Flows, and the Penrose Inequality in General Relativity.” *Notices of the American Mathematical Society*, vol. 49, no. 11, 2002, pp. 1372–81.

Bray, H. L. “Proof of the riemannian penrose inequality using the positive mass theorem.” *Journal of Differential Geometry*, vol. 59, no. 2, Jan. 2001, pp. 177–267. *Scopus*, doi:10.4310/jdg/1090349428.
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Bray, H., et al. “Wavelet variations on the Shannon sampling theorem.” *Bio Systems*, vol. 34, no. 1–3, Jan. 1995, pp. 249–57. *Epmc*, doi:10.1016/0303-2647(94)01457-i.
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Bray, Hubert, et al. *Proof of Bishop's volume comparison theorem using singular soap bubbles*.

Bray, Hubert, and Daniel Stern. *Scalar curvature and harmonic one-forms on three-manifolds with boundary*.