Math @ Duke

Papers Published
 H.L. Bray and A. R. Parry, Modeling Wave Dark Matter in Dwarf Spheroidal Galaxies,
Proceedings of IARD 2014, Journal of Physics: Conference Series, vol. 615
(2015) [available here]
 H.L. Bray and J.L. Jauregui, A Geometric Theory of Zero Area Singularities in General Relativity,
Asian Journal of Mathematics, vol. 17 no. 3
(September, 2013),
pp. 525560 [arXiv:0909.0522v1]
 H.L. Bray, On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity,
AMS Contemporary Mathematics Volume, "Geometric Analysis, Mathematical Relativity, and Nonlinear Partial Differential Equations", vol. 599
(2013), American Mathematical Society [html]
 H.L. Bray and M.A. Khuri, P.D.E.'s Which Imply the Penrose Conjecture,
Asian Journal of Mathematics, vol. 15 no. 4
(December, 2011),
pp. 54, International Press, ISSN 10936106 [pdf] [author's comments]
 H.L. Bray, On the Positive Mass, Penrose, and ZAS Inequalities in General Dimension,
in Surveys in Geometric Analysis and Relativity in Honor of Richard Schoen's 60th Birthday, edited by Hubert L. Bray and William P. Minicozzi
(2011), Higher Education Press and International Press, Beijing and Boston [arXiv:1101.2230v1], [pdf] [author's comments]
 H.L. Bray and M.A. Khuri, A Jang Equation Approach to the Penrose Inequality,
Discrete and Continuous Dynamical Systems A, vol. 27 no. 2
(June, 2010) [arXiv:0910.4785v1]
 H.L. Bray, S. Brendle, M. Eichmair, A. Neves, AreaMinimizing Projective Planes in 3Manifolds,
Communications in Pure and Applied Mathematics
(2010) [arXiv:0909.1665v1]
 H.L. Bray, S. Brendle, A. Neves, Rigidity of AreaMinimizing TwoSpheres in ThreeManifolds,
Communications in Analysis and Geometry
(2010) [arXiv:1002.2814]
 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. 81106 [arXiv:0705.1128v1], [pdf]
 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]
 H.L. Bray, S. Hayward, M. Mars, W. Simon, Generalized Inverse Mean Curvature Flows in Spacetime,
Communications in Mathematical Physics, vol. 272 no. 1
(May, 2007),
pp. 119138 [arXiv:grqc/0603014v1]
 H.L. Bray, The Positve Energy Theorem and Other Inequalities in GR,
in The Encyclopedia of Mathematical Physics
(2005)
 H.L. Bray and A. Neves, Classification of Prime 3Manifolds with Yamabe Invariant Greater than RP^3,
Annals of Mathematics, vol. 159 no. 1
(2004),
pp. 407424 [p09]
 H.L. Bray and P.T. Chrusciel, The Penrose Inequality,
in The Einstein Equations and the Large Scale Behavior of Gravitational Fields (50 Years of the Cauchy Problem in General Relativity), edited by P.T. Chrusciel and H.F. Friedrich
(2004), Birkhauser [arXiv:grqc/0312047v2]
 H.L. Bray, A Family of Quasilocal Mass Functionals with Monotone Flows,
in Proceedings of the 14th International Congress on Mathematical Physics, Lisbon, Portugal, 2003, edited by JeanClaude Zambrini
(2003) [Family%20of%20Quasilocal%20Mass%20Functionals%20with%20Monotone%20Flows&f=false]
 H.L. Bray 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. 9991016
 H.L. Bray, Black Holes, Geometric Flows, and the Penrose Inequality in General Relativity,
Notices of the American Mathematical Society, vol. 49 no. 11
(2002),
pp. 13721381 [pdf]
 H. L. Bray and F. Finster, Curvature Estimates and the Positive Mass Theorem,
Communications in Analysis and Geometry, vol. 10 no. 2
(2002),
pp. 291306 [arXiv:math/9906047v3]
 H. L. Bray and F. Morgan, An Isoperimetric Comparison Theorem for Schwarzschild Space and Other Manifolds,
Proceedings of the American Mathematical Society, vol. 130 no. 5
(2002),
pp. 14671472 [pdf]
 H.L. Bray, Black Holes and the Penrose Inequality in General Relativity,
in Proceedings of the International Congress of Mathematicians, Beijing, China, 2002, vol. 2
(2002),
pp. 257272 [arXiv:math/0304261v1]
 H. L. Bray, Proof of the Riemannian Penrose Inequality Using the Positive Mass Theorem,
Journal of Differential Geometry, vol. 59 no. 2
(2001),
pp. 177267 [arXiv:math/9911173v1], [pdf]
 H. L. Bray and R.M. Schoen, Recent Proofs of the Riemannian Penrose Conjecture,
in Current Developments in Mathematics, 1999 (Cambridge, MA)
(1999),
pp. 136, Int. Press, Somerville, MA
 H.L. Bray, K. McCormick, R.O. Wells, Jr., Xiaodong Zhou, Wavelet Variations on the Shannon Sampling Theorem,
Biosystems, vol. 34
(1995),
pp. 249257, Elsevier Science Ireland [science] [author's comments]
Papers Accepted
 H.L. Bray and J. L. Jauregui, Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass,
Communications in Mathematical Physics
(April, 2014) [arXiv:1310.8638 [math.DG]], [8638]
 H.L. Bray and J. L. Jauregui, On Curves with Nonnegative Torsion,
Archiv der Mathematik
(December, 2013) [arXiv:1312.5171 [math.DG]], [5171]
Preprints
 H.L. Bray and A.S. Goetz, Wave Dark Matter and the TullyFisher Relation
(September, 2014) [arXiv:1409.7347], [html]
 H.L. Bray, J. L. Jauregui, M. Mars, Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass II
(February, 2014) [arXiv:1402.3287 [math.DG]], [3287] [abs]
 H.L. Bray, On Wave Dark Matter, Shells in Elliptical Galaxies, and the Axioms of General Relativity
(December 22, 2012) [html]
Other
 H.L. Bray, The Penrose Inequality in General Relativity and Volume Comparison Theorems Involving Scalar Curvature
(1997) (thesis, Stanford University.) [arXiv:0902.3241v1]


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

