Math @ Duke

Papers Published
 Bray, H; Hirsch, S; Kazaras, D; Khuri, M; Zhang, Y, Spacetime Harmonic Functions and Applications to Mass, edited by Gromov, ML; Lawson, HB,
Perspectives in Scalar Curvature
(February, 2023), World Scientific [abs]
 Bray, H; Stern, D, Scalar curvature and harmonic oneforms on threemanifolds with boundary
(November, 2019)
 Bray, H; Stern, D; Khuri, M; Kazaras, D, Harmonic Functions and The Mass of 3Dimensional Asymptotically Flat Riemannian Manifolds
(November, 2019)
 Bray, H; Liu, Z; Zhang, Y; Gui, F, Proof of Bishop's volume comparison theorem using singular soap bubbles
(March, 2019)
 Bray, H; Hamm, B; Hirsch, S; Wheeler, J; Zhang, Y, Flatly foliated relativity,
Pure and Applied Mathematics Quarterly, vol. 15 no. 2
(January, 2019),
pp. 707747, International Press of Boston [doi] [abs]
 Bray, HL; Minicozzi, WP, The mathematics of richard schoen,
Notices of the American Mathematical Society, vol. 65 no. 12
(December, 2018),
pp. 13491176, American Mathematical Society (AMS) [doi]
 Bray, HL; Minicozzi, WP, Preface,
Notices of the American Mathematical Society, vol. 65 no. 11
(December, 2018),
pp. 14121413 [doi]
 Bray, H; Roesch, H, Proof of a Null Geometry Penrose Conjecture,
Notices of the American Mathematical Society., vol. 65
(February, 2018), American Mathematical Society
 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
(June, 2016),
pp. 14571475, Springer Nature, ISSN 14240637 [arXiv:1402.3287 [math.DG]], [3287], [doi] [abs]
 MartinezMedina, LA; Bray, H; Mattos, T, On wave dark matter in spiral and barred galaxies, vol. 2015 no. 12
(December, 2015),
pp. 025025, IOP Publishing [arXiv:1505.07154], [1505.07154], [doi] [abs]
 Bray, HL; Jauregui, JL, On curves with nonnegative torsion,
Archiv Der Mathematik, vol. 104 no. 6
(June, 2015),
pp. 561575, Springer Nature, ISSN 0003889X [arXiv:1312.5171 [math.DG]], [c8d239381b86496b96d95ff26f1061eb], [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, 2015),
pp. 285307, Springer Nature, ISSN 00103616 [arXiv:1310.8638 [math.DG]], [8638], [doi] [abs]
 Bray, HL; Parry, AR, Modeling wave dark matter in dwarf spheroidal galaxies,
Journal of Physics: Conference Series, vol. 615 no. 1
(2015),
pp. 012001012001, IOP Publishing, ISSN 17426588 [Gateway.cgi], [doi] [abs]
 Bray, H; Goetz, AS, Wave Dark Matter and the TullyFisher Relation
(September, 2014) [arXiv:1409.7347], [7347] [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, HL; Jauregui, JL, A geometric theory of zero area singularities in general relativity,
Asian Journal of Mathematics, vol. 17 no. 3
(2013),
pp. 525560, International Press of Boston, ISSN 10936106 [arXiv:0909.0522v1], [doi] [abs]
 Bray, H, On Wave Dark Matter, Shells in Elliptical Galaxies, and the Axioms of General Relativity
(December, 2012) [pdf] [abs]
 Bray, HL; Khuri, MA, P.D.E.'s Which Imply the Penrose Conjecture,
Asian Journal of Mathematics, vol. 15 no. 4
(December, 2011),
pp. 54, International Press
 Bray, HL; Khuri, MA, P. D. E. 'S which imply the penrose conjecture,
Asian Journal of Mathematics, vol. 15 no. 4
(January, 2011),
pp. 557610, International Press of Boston, ISSN 10936106 [pdf], [doi] [abs] [author's comments]
 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, H; Brendle, S; Eichmair, M; Neves, A, AreaMinimizing Projective Planes in 3Manifolds,
Communications on Pure and Applied Mathematics, vol. 63 no. 9
(September, 2010),
pp. 12371247, WILEY, ISSN 00103640 [arXiv:0909.1665v1], [doi] [abs]
 Bray, HL; Khuri, MA, A jang equation approach to the penrose inequality,
Discrete and Continuous Dynamical Systems Series A, vol. 27 no. 2
(June, 2010),
pp. 741766, American Institute of Mathematical Sciences (AIMS), ISSN 10780947 [arXiv:0910.4785v1], [doi] [abs]
 Bray, H; Brendle, S; Neves, A, Rigidity of areaminimizing twospheres in threemanifolds,
Communications in Analysis and Geometry, vol. 18 no. 4
(January, 2010),
pp. 821830, International Press of Boston, ISSN 10198385 [arXiv:1002.2814], [doi] [abs]
 Bray, HL; Lee, DA, On the Riemannian Penrose inequality in dimensions less than eight,
Duke Mathematical Journal, vol. 148 no. 1
(May, 2009),
pp. 81106, Duke University Press, ISSN 00127094 [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. 459475, Springer Nature, ISSN 00209910 [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. 119138, Springer Nature, ISSN 00103616 [arXiv:grqc/0603014v1], [doi] [abs]
 Bray, H, A Family of Quasilocal Mass Functionals with Monotone Flows, edited by Zambrini, JC,
Proceedings of the 14th International Congress on Mathematical Physics
(January, 2006),
pp. 323329, World Scientific, ISBN 981256201X [doi] [abs]
 H.L. Bray, The Positve Energy Theorem and Other Inequalities in GR,
in The Encyclopedia of Mathematical Physics
(2005)
 Bray, H, The Positve Energy Theorem and Other Inequalities,
in The Encyclopedia of Mathematical Physics
(2005)
 Bray, HL; Neves, A, Classification of Prime 3Manifolds with Yamabe Invariant Greater than RP^3,
Annals of Mathematics, vol. 159 no. 1
(January, 2004),
pp. 407424, Annals of Mathematics, Princeton U [p09], [doi] [abs]
 Bray, H, Geometric Flows and the Penrose Inequality,
in Encyclopedia of Mathematical Physics: FiveVolume Set
(January, 2004),
pp. 510520, ISBN 9780125126663 [doi]
 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: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]
 Bray, H; Morgan, F, An isoperimetric comparison theorem for schwarzschild space and other manifolds,
Proceedings of the American Mathematical Society, vol. 130 no. 5
(January, 2002),
pp. 14671472 [pdf], [doi] [abs]
 Bray, H; Finster, F, Curvature estimates and the Positive Mass Theorem,
Communications in Analysis and Geometry, vol. 10 no. 2
(January, 2002),
pp. 291306, International Press of Boston [arXiv:math/9906047v3], [doi] [abs]
 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. 257272 [arXiv:math/0304261v1], [0304261v1]
 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. 13721381 [pdf]
 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. 9991016, International Press of Boston [doi]
 Bray, HL, Proof of the riemannian penrose inequality using the positive mass theorem,
Journal of Differential Geometry, vol. 59 no. 2
(January, 2001),
pp. 177267, International Press of Boston [arXiv:math/9911173v1], [pdf], [doi] [abs]
 Bray, H; Schoen, RM, Recent Proofs of the Riemannian Penrose Conjecture,
in Current Developments in Mathematics
(1999),
pp. 136, International Press
 Bray, H; McCormick, K; Wells, RO; Zhou, XD, Wavelet variations on the Shannon sampling theorem.,
Biosystems, vol. 34 no. 13
(January, 1995),
pp. 249257, Elsevier Science Ireland, ISSN 03032647 [science], [doi] [abs] [author's comments]
Other
 Bray, H, 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

