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Hubert Bray

Professor of Mathematics
Mathematics
Box 90320, Durham, NC 27708-0320
189 Physics Bldg, Durham, NC 27710

Selected Publications


Spacetime Harmonic Functions and Applications to Mass

Other Perspectives in Scalar Curvature · February 1, 2023 In the pioneering work of Stern, level sets of harmonic functions have been shown to be an effective tool in the study of scalar curvature in dimension 3. Generalizations of this idea, utilizing level sets of so called spacetime harmonic functions as well ... Link to item Cite

Flatly foliated relativity

Journal Article Pure and Applied Mathematics Quarterly · January 1, 2019 Flatly Foliated Relativity (FFR) is a new theory which conceptually lies between Special Relativity (SR) and General Relativity (GR), in which spacetime is foliated by flat Euclidean spaces. While GR is based on the idea that “matter curves spacetime”, FFR ... Full text Cite

The mathematics of richard schoen

Journal Article Notices of the American Mathematical Society · December 1, 2018 Full text Cite

Preface

Journal Article Notices of the American Mathematical Society · December 1, 2018 Full text Cite

Proof of a Null Geometry Penrose Conjecture

Journal Article Notices of the American Mathematical Society. · February 1, 2018 Cite

Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass II

Journal Article Annales Henri Poincare · June 1, 2016 In this sequel paper, we give a shorter, second proof of the monotonicity of the Hawking mass for time flat surfaces under spacelike uniformly area expanding flows in spacetimes that satisfy the dominant energy condition. We also include a third proof whic ... Full text Cite

On curves with nonnegative torsion

Journal Article Archiv der Mathematik · June 29, 2015 We provide new results and new proofs of results about the torsion of curves in $${\mathbb{R}^3}$$R3. Let $${\gamma}$$γ be a smooth curve in $${\mathbb{R}^3}$$R3 that is the graph over a simple closed curve in $${\mathbb{R}^2}$$R2 with positive curvature. ... Full text Cite

Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass

Journal Article Communications in Mathematical Physics · April 1, 2015 We identify a condition on spacelike 2-surfaces in a spacetime that is relevant to understanding the concept of mass in general relativity. We prove a formula for the variation of the spacetime Hawking mass under a uniformly area expanding flow and show th ... Full text Cite

Modeling wave dark matter in dwarf spheroidal galaxies

Conference 9TH BIENNIAL CONFERENCE ON CLASSICAL AND QUANTUM RELATIVISTIC DYNAMICS OF PARTICLES AND FIELDS (IARD 2014) · 2015 Full text Cite

Wave Dark Matter and the Tully-Fisher Relation

Journal Article · September 2014 Preprint ... Link to item Cite

A geometric theory of zero area singularities in general relativity

Journal Article Asian Journal of Mathematics · 2013 The Schwarzschild spacetime metric of negative mass is well-known to contain a naked singularity. In a spacelike slice, this singularity of the metric is characterized by the property that nearby surfaces have arbitrarily small area. We develop a theory of ... Full text Cite

On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity

Journal Article AMS Contemporary Mathematics Volume · 2013 Link to item Cite

P.D.E.'s Which Imply the Penrose Conjecture

Journal Article Asian Journal of Mathematics · December 2011 Link to item Cite

P. D. E. 'S which imply the penrose conjecture

Journal Article Asian Journal of Mathematics · January 1, 2011 In this paper, we show how to reduce the Penrose conjecture to the known Riemannian Penrose inequality case whenever certain geometrically motivated systems of equations can be solved. Whether or not these special systems of equations have general existenc ... Full text Cite

Area-Minimizing Projective Planes in 3-Manifolds

Journal Article Communications on Pure and Applied Mathematics · September 1, 2010 Let (M, g) be a compact Riemannian manifold of dimension 3, and let F denote the collection of all embedded surfaces homeomorphic to R{double-struck}P{double-struck}2. We study the infimum of the areas of all surfaces in F . This quantity is related to the ... Full text Cite

Spacetime Harmonic Functions and Applications to Mass

Other Perspectives in Scalar Curvature · February 1, 2023 In the pioneering work of Stern, level sets of harmonic functions have been shown to be an effective tool in the study of scalar curvature in dimension 3. Generalizations of this idea, utilizing level sets of so called spacetime harmonic functions as well ... Link to item Cite

Flatly foliated relativity

Journal Article Pure and Applied Mathematics Quarterly · January 1, 2019 Flatly Foliated Relativity (FFR) is a new theory which conceptually lies between Special Relativity (SR) and General Relativity (GR), in which spacetime is foliated by flat Euclidean spaces. While GR is based on the idea that “matter curves spacetime”, FFR ... Full text Cite

The mathematics of richard schoen

Journal Article Notices of the American Mathematical Society · December 1, 2018 Full text Cite

Preface

Journal Article Notices of the American Mathematical Society · December 1, 2018 Full text Cite

Proof of a Null Geometry Penrose Conjecture

Journal Article Notices of the American Mathematical Society. · February 1, 2018 Cite

Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass II

Journal Article Annales Henri Poincare · June 1, 2016 In this sequel paper, we give a shorter, second proof of the monotonicity of the Hawking mass for time flat surfaces under spacelike uniformly area expanding flows in spacetimes that satisfy the dominant energy condition. We also include a third proof whic ... Full text Cite

On curves with nonnegative torsion

Journal Article Archiv der Mathematik · June 29, 2015 We provide new results and new proofs of results about the torsion of curves in $${\mathbb{R}^3}$$R3. Let $${\gamma}$$γ be a smooth curve in $${\mathbb{R}^3}$$R3 that is the graph over a simple closed curve in $${\mathbb{R}^2}$$R2 with positive curvature. ... Full text Cite

Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass

Journal Article Communications in Mathematical Physics · April 1, 2015 We identify a condition on spacelike 2-surfaces in a spacetime that is relevant to understanding the concept of mass in general relativity. We prove a formula for the variation of the spacetime Hawking mass under a uniformly area expanding flow and show th ... Full text Cite

Modeling wave dark matter in dwarf spheroidal galaxies

Conference 9TH BIENNIAL CONFERENCE ON CLASSICAL AND QUANTUM RELATIVISTIC DYNAMICS OF PARTICLES AND FIELDS (IARD 2014) · 2015 Full text Cite

Wave Dark Matter and the Tully-Fisher Relation

Journal Article · September 2014 Preprint ... Link to item Cite

A geometric theory of zero area singularities in general relativity

Journal Article Asian Journal of Mathematics · 2013 The Schwarzschild spacetime metric of negative mass is well-known to contain a naked singularity. In a spacelike slice, this singularity of the metric is characterized by the property that nearby surfaces have arbitrarily small area. We develop a theory of ... Full text Cite

On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity

Journal Article AMS Contemporary Mathematics Volume · 2013 Link to item Cite

P.D.E.'s Which Imply the Penrose Conjecture

Journal Article Asian Journal of Mathematics · December 2011 Link to item Cite

P. D. E. 'S which imply the penrose conjecture

Journal Article Asian Journal of Mathematics · January 1, 2011 In this paper, we show how to reduce the Penrose conjecture to the known Riemannian Penrose inequality case whenever certain geometrically motivated systems of equations can be solved. Whether or not these special systems of equations have general existenc ... Full text Cite

Area-Minimizing Projective Planes in 3-Manifolds

Journal Article Communications on Pure and Applied Mathematics · September 1, 2010 Let (M, g) be a compact Riemannian manifold of dimension 3, and let F denote the collection of all embedded surfaces homeomorphic to R{double-struck}P{double-struck}2. We study the infimum of the areas of all surfaces in F . This quantity is related to the ... Full text Cite

A jang equation approach to the penrose inequality

Journal Article Discrete and Continuous Dynamical Systems · June 1, 2010 We introduce a generalized version of the Jang equation, designed for the general case of the Penrose Inequality in the setting of an asymptotically flat space-like hypersurface of a spacetime satisfying the dominant energy condition. The appropriate exist ... Full text Cite

Rigidity of area-minimizing two-spheres in three-manifolds

Journal Article Communications in Analysis and Geometry · January 1, 2010 We give a sharp upper bound for the area of a minimal two-sphere in a three-manifold (M,g) with positive scalar curvature. If equality holds, we show that the universal cover of (M,g) is isometric to a cylinder. ... Full text Cite

On the Riemannian Penrose inequality in dimensions less than eight

Journal Article Duke Mathematical Journal · May 1, 2009 The positive mass theorem states that a complete asymptotically flat manifold of nonnegative scalar curvature has nonnegative mass and that equality is achieved only for the Euclidean metric. The Riemannian Penrose inequality provides a sharp lower bound f ... Full text Cite

On the capacity of surfaces in manifolds with nonnegative scalar curvature

Journal Article Inventiones Mathematicae · June 1, 2008 Given a surface in an asymptotically flat 3-manifold with nonnegative scalar curvature, we derive an upper bound for the capacity of the surface in terms of the area of the surface and the Willmore functional of the surface. The capacity of a surface is de ... Full text Cite

Generalized inverse mean curvature flows in spacetime

Journal Article Communications in Mathematical Physics · May 1, 2007 Motivated by the conjectured Penrose inequality and by the work of Hawking, Geroch, Huisken and Ilmanen in the null and the Riemannian case, we examine necessary conditions on flows of two-surfaces in spacetime under which the Hawking quasilocal mass is mo ... Full text Cite

Geometric Flows and the Penrose Inequality

Chapter · January 1, 2004 In a paper, R Penrose (1973) made a physical argument that the total mass of a spacetime which contains black holes with event horizons of total area A should be at least. ... Full text Cite

Classification of Prime 3-Manifolds with Yamabe Invariant Greater than RP^3

Journal Article Annals of Mathematics · January 2004 In this paper we compute the σ-invariants (sometimes also called the smooth Yamabe invariants) of RP3 and RP2×S1 (which are equal) and show that the only prime 3-manifolds with larger σ-invariants are S3, S2×S1, and S2×~S1 (the nonorientable S2 bundle over ... Link to item Cite

Black Holes and the Penrose Inequality in General Relativity

Conference Proceedings of the International Congress of Mathematicians · 2002 Link to item Cite

Superharmonic Functions in R^n and the Penrose Inequality in General Relativity

Journal Article Communications in Analysis and Geometry · 2002 Cite

Black Holes, Geometric Flows, and the Penrose Inequality in General Relativity

Journal Article Notices of the American Mathematical Society · 2002 Cite

Curvature estimates and the Positive Mass Theorem

Journal Article Communications in Analysis and Geometry · January 1, 2002 The Positive Mass Theorem implies that any smooth, complete, asymptotically flat 3-manifold with non-negative scalar curvature which has zero total mass is isometric to (ℝ3 δij). In this paper, we quantify this statement using spinors and prove that if a c ... Full text Cite

An isoperimetric comparison theorem for schwarzschild space and other manifolds

Conference Proceedings of the American Mathematical Society · January 1, 2002 We give a very general isoperimetric comparison theorem which, as an important special case, gives hypotheses under which the spherically symmetric (n - 1)-spheres of a spherically symmetric n-manifold are isoperimetric hypersurfaces, meaning that they min ... Full text Cite

Proof of the riemannian penrose inequality using the positive mass theorem

Journal Article Journal of Differential Geometry · January 1, 2001 We prove the Riemannian Penrose Conjecture, an important case of a conjecture [41] made by Roger Penrose in 1973, by defining a new flow of metrics. This flow of metrics stays inside the class of asymptotically flat Riemannian 3-manifolds with nonnegative ... Full text Cite

Wavelet variations on the Shannon sampling theorem.

Journal Article Bio Systems · January 1995 The Shannon sampling theorem asserts that a continuous square-integrable function on the real line which has a compactly supported Fourier transform is uniquely determined by its restriction to a uniform lattice of points whose density is determined by the ... Full text Cite

A Family of Quasi-local Mass Functionals with Monotone Flows

Conference Proceedings of the 14th International Congress on Mathematical Physics Cite

Classification of Preferential Ballot Voting Methods

Other Constitutional Political Economy Cite