Professor H. L. Bray
the mathematics required to understand gravity as the curvature of
spacetime, and whose further development is essential for a deeper
understanding of physics
Professor Bray's research in geometric analysis involves minimal
surfaces, scalar curvature, conformal geometry, null geometry,
geometric flows, and harmonic functions, among other topics. In his
thesis, he proved a volume comparison theorem for scalar curvature
which generalizes Bishop's theorem (for Ricci curvature) in three
dimensions. Following an idea proposed by Richard Schoen, Andre Neves
and he were the first to compute the Yamabe invariant of RP^3, enabling
them to completely classify 3-manifolds with greater Yamabe invariant.
With Simon Brendle, Michael Eichmair, and Andre Neves, Professor Bray
proved a variety of rigidity theorems for compact manifolds, relating
scalar curvature to the area of minimal surfaces.
In addition, Professor Bray's proof of the Riemannian Penrose
Conjecture in dimension 3, and in dimensions less than 8 with Dan Lee,
is a very interesting result about the relationship between scalar
curvature and minimal surfaces on asymptotically flat manifolds. This
result may be viewed entirely in geometric terms, with the happy
coincidence that it also solved a major open problem about black holes,
conjectured by Sir Roger Penrose in 1973.
More generally, most of Professor Bray's work, including his
research in General Relativity and ideas relating to Dark Matter, may
be thought of as topics in Geometric Analysis. If you are a student at
Duke, consider taking Math 421, undergraduate differential geometry,
with Professor Bray, followed by Math 621, graduate differential
geometry. These courses will give you the background you need to use
differential geometry as a tool for understanding general relativity
and the large-scale structure of the universe.
describes Professor Bray's work in 2014 on the Hawking mass and time flat surfaces in
spacetimes, joint with Jauregui and Mars.
For a complete list of publications, grants, awards, and professional activities, visit Professor Bray's Duke University web page or view this computer generated curriculum vitae.