9704338 Kapouleas The proposal consists of two somewhat distinct groups of projects. The first group of project deals with various geometric constructions by singular pertubation methods. These include constructions using desingularization of intersecting minimal surfaces, minimal hypersurfaces and constant mean curvature hypersurfaces in higher dimensional Euclidean space, and Einstein four-manifolds. The second group of projects lie in the area of general relativity. In particular, the PI, in collaboration with Christodoulou, will try to settle uniqueness and stability questions for the Kerr and Schwarzschild black holes. Minimal surfaces arise as various physical surfaces; they have the remarkable property of minimizing the surface area amongst all surfaces bounded by the same spatial contour. Minimal surfaces can also used to model condensed matter. Stability questions for black holes, which involve examining the interaction of a black hole with weak gravitational waves, have important applications in cosmology.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
9704338
Program Officer
Christopher W. Stark
Project Start
Project End
Budget Start
1997-07-01
Budget End
2001-09-30
Support Year
Fiscal Year
1997
Total Cost
$140,000
Indirect Cost
Name
Brown University
Department
Type
DUNS #
City
Providence
State
RI
Country
United States
Zip Code
02912