Regularity Results and Function Theory

摘要建议：DMS-9803253首席研究员：托拜厄斯·科尔丁拟议的研究包括对具有Ricci曲率界的流形的研究，函数论，以及更广泛的流形上丛的截面理论的研究。最后，所提出的研究将包括三个流形中极小曲面的紧性和收敛结果及其可能的拓扑应用。几何分析中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。在拟议的研究中，PI打算在两种主要情况下实现这一点，第一种情况是具有Ricci曲率界的流形，第二种情况是三种流形。

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.