Regularity Results and Function Theory

摘要提案：DMS-9803253首席研究员：Tobias Colding提议的研究包括具有Ricci曲率界的流形，函数理论和更一般的流形上束的截面理论。最后提出的研究将包括三个流形最小曲面的紧性和收敛性结果及其可能的拓扑应用。几何分析的一个基本问题是试图理解拓扑、几何和流形分析之间的关系。在提出的研究中，PI打算尝试在两种主要情况下实现这一目标，第一种是具有里奇曲率界限的流形，第二种是三个流形。

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.