**Keywords:**- Analysis, General relativity (Physics), Geometric analysis, Geometry, Mathematical physics, Theoretical astrophysics

**Representative Publications**- Martinez-Medina, LA; Bray, HL; Matos, T,
*On wave dark matter in spiral and barred galaxies*, Journal of Cosmology and Astroparticle Physics, vol. 2015 no. 12 (December, Accepted, 2015), pp. 025-025 [arXiv:1505.07154], [1505.07154], [doi] - Bray, H; Goetz, AS,
*Wave Dark Matter and the Tully-Fisher Relation*(Preprint, September, 2014) [arXiv:1409.7347], [7347] [abs] - Bray, HL; Jauregui, JL; Mars, M,
*Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass II*, Annales Henri PoincarĂ©, vol. 17 no. 6 (July 26, 2015), pp. 1457-1475, Springer Basel, ISSN 1424-0637 [arXiv:1402.3287 [math.DG]], [3287], [doi] [abs] - Bray, HL; Jauregui, JL,
*Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass*, Communications in Mathematical Physics, vol. 335 no. 1 (April, 2014), pp. 285-307, ISSN 0010-3616 [arXiv:1310.8638 [math.DG]], [8638], [doi] - Bray, HL; Jauregui, JL,
*On curves with nonnegative torsion*, Archiv der Mathematik, vol. 104 no. 6 (2015), pp. 561-575, ISSN 0003-889X [arXiv:1312.5171 [math.DG]], [c8d239381b86496b96d95ff26f1061eb], [doi] - Bray, HL; Parry, AR,
*Modeling wave dark matter in dwarf spheroidal galaxies*, Journal of Physics, vol. 615 (2015), ISSN 1742-6588 [Gateway.cgi], [doi] - Bray, H,
*On Wave Dark Matter, Shells in Elliptical Galaxies, and the Axioms of General Relativity*(Preprint, December 22, 2012) [pdf] [abs] - Bray, HL,
*On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity*, AMS Contemporary Mathematics Volume, vol. 599 no. Geometric Analysis, Mathematical Relativ (2013), American Mathematical Society [arXiv:1004.4016], [html] - Bray, H,
*On the Positive Mass, Penrose, and ZAS Inequalities in General Dimension*, in Surveys in Geometric Analysis and Relativity in Honor of Richard Schoenâ€™s 60th Birthday, edited by Bray, H; Minicozzi, W (2011), Higher Education Press and International Press, Beijing and Boston [arXiv:1101.2230v1], [2230] [author's comments] - Bray, HL; Khuri, MA,
*P. D. E. 'S which imply the penrose conjecture*, Asian Journal of Mathematics, vol. 15 no. 4 (December, 2011), pp. 557-610, International Press, ISSN 1093-6106 [pdf] [abs] [author's comments] - Bray, HL; Khuri, MA,
*A jang equation approach to the penrose inequality*, Discrete and Continuous Dynamical Systems, vol. 27 no. 2 (June, 2010), pp. 741-766, ISSN 1078-0947 [arXiv:0910.4785v1], [doi] [abs] - Bray, H; Brendle, S; Eichmair, M; Neves, A,
*Area-Minimizing Projective Planes in 3-Manifolds*, Communications on Pure & Applied Mathematics, vol. 63 no. 9 (2010), pp. 1237-1247, ISSN 0010-3640 [arXiv:0909.1665v1], [doi] [abs] - Bray, H; Brendle, S; Neves, A,
*Rigidity of area-minimizing two-spheres in three-manifolds*, Communications in Analysis and Geometry, vol. 18 no. 4 (2010), pp. 821-830, ISSN 1019-8385 [arXiv:1002.2814] [abs] - Bray, HL; Jauregui, JL,
*A geometric theory of zero area singularities in general relativity*, Asian Journal of Mathematics, vol. 17 no. 3 (September, 2013), pp. 525-560, ISSN 1093-6106 [arXiv:0909.0522v1], [doi] [abs] - Bray, HL; Lee, DA,
*On the Riemannian Penrose inequality in dimensions less than eight*, Duke Mathematical Journal, vol. 148 no. 1 (2009), pp. 81-106, ISSN 0012-7094 [arXiv:0705.1128v1], [pdf], [doi] [abs] - Bray, H; Miao, P,
*On the capacity of surfaces in manifolds with nonnegative scalar curvature*, Inventiones mathematicae, vol. 172 no. 3 (June, 2008), pp. 459-475, ISSN 0020-9910 [arXiv:0707.3337v1], [doi] [abs] - Bray, H; Hayward, S; Mars, M; Simon, W,
*Generalized inverse mean curvature flows in spacetime*, Communications in Mathematical Physics, vol. 272 no. 1 (May, 2007), pp. 119-138, ISSN 0010-3616 [arXiv:gr-qc/0603014v1], [doi] [abs] - Bray, HL; Neves, A,
*Classification of Prime 3-Manifolds with Yamabe Invariant Greater than RP^3*, Annals of Mathematics, vol. 159 no. 1 (January, 2004), pp. 407-424 [p09] [abs] - Bray, H,
*The Positve Energy Theorem and Other Inequalities*, in The Encyclopedia of Mathematical Physics (2005) - 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) [Family%20of%20Quasi-local%20Mass%20Functionals%20with%20Monotone%20Flows&f=false] - Bray, H; Finster, F,
*Curvature estimates and the Positive Mass Theorem*, Communications in Analysis and Geometry, vol. 10 no. 2 (2002), pp. 291-306 [arXiv:math/9906047v3] [abs] - Bray, HL; Iga, K,
*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; Morgan, F,
*An isoperimetric comparison theorem for schwarzschild space and other manifolds*, Proceedings of the American Mathematical Society, vol. 130 no. 5 (2002), pp. 1467-1472 [pdf], [doi] [abs] - Bray, HL,
*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], [pdf] [abs] - Bray, H; Schoen, RM,
*Recent Proofs of the Riemannian Penrose Conjecture*, in Current Developments in Mathematics (1999), pp. 1-36, International Press - H.L. Bray,
*The Positve Energy Theorem and Other Inequalities in GR*, in The Encyclopedia of Mathematical Physics (2005) - Bray, H; Chrusciel, PT,
*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 Chrusciel, PT; Friedrich, HF (2004), Birkhauser [arXiv:gr-qc/0312047v2] - Bray, HL,
*Black Holes, Geometric Flows, and the Penrose Inequality in General Relativity*, Notices of the American Mathematical Society, vol. 49 no. 11 (2002), pp. 1372-1381 [pdf] - Bray, H,
*Black Holes and the Penrose Inequality in General Relativity*, in Proceedings of the International Congress of Mathematicians, Beijing, China, 2002, Proceedings of the International Congress of Mathematicians, vol. 2 (2002), pp. 257-272 [arXiv:math/0304261v1], [0304261v1] - Bray, H; McCormick, K; Jr, ROW; Zhou, X-D,
*Wavelet variations on the Shannon sampling theorem*, BioSystems, vol. 34 no. 1-3 (1995), pp. 249-257, Elsevier Science Ireland, ISSN 0303-2647 [science], [doi] [abs] [author's comments] - Bray, H,
*The Penrose Inequality in General Relativity and Volume Comparison Theorems Involving Scalar Curvature*(1997) (thesis, Stanford University.) [arXiv:0902.3241v1]

- Martinez-Medina, LA; Bray, HL; Matos, T,