Abstract Proposal: DMS-9803253 Principal Investigator: Tobias Colding The proposed investigation includes research on manifolds with Ricci curvature bounds, function theory and more generally theory of sections of bundles on manifolds. Finally the proposed research will include compactness and convergence results for minimal surfaces in three manifolds and their possible topological applications. One of the fundamental problems in geometric analysis is to try to understand the relationship between the topology, the geometry, and the analysis of manifolds. In the proposed research the PI intends to try to accomplish this in two main cases, the first being for manifolds with Ricci curvature bounds and the second being for three manifolds.
