Michael Anderson will carry out research in the following areas of global differential geometry: (1)The Laplace-Beltrami operator on complete Riemannian manifolds; (2)Minimal varieties, including relations with curvature integrals and Riemannian geometry; (3)Structure of manifolds of non-positive curvature and without conjugate points; (4)Structure of manifolds of non- negative Ricci and scalar curvature. In particular he will investigate the uniqueness of the tangent cone at infinity of a complete minimal surface of bounded total Gauss-Kronecker curvature. He will also continue his investigations of Hopf's conjecture that a Riemannian metric on on the torus without conjugate points is flat. The basic objective of the research concerning manifolds of non-positive curvature is to find relations between the fundamental group and the geometric properties of the manifold.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
8701137
Program Officer
Trudy T. Sensibaugh
Project Start
Project End
Budget Start
1987-06-01
Budget End
1988-06-15
Support Year
Fiscal Year
1987
Total Cost
$32,800
Indirect Cost
Name
California Institute of Technology
Department
Type
DUNS #
City
Pasadena
State
CA
Country
United States
Zip Code
91125