Regularity Results and Function Theory

摘要 提案：DMS-9803253主要研究者：Tobias Colding 建议的调查包括研究流形与里奇 曲率界限，函数理论和更一般的理论， 流形上丛的截面 最后，研究将 包括最小曲面紧性和收敛性结果， 三个流形及其可能的拓扑应用。 几何分析中的一个基本问题是， 了解拓扑结构、几何结构和 流形的分析 在拟定的研究中，PI打算 尝试在两个主要情况下实现这一点，第一个是为了 流形与里奇曲率界和第二个是三个 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.