Research in Geometric Analysis

项目编号：dms -9971574首席研究员：F. Reese harvey本项目由三部分组成。首先，对推进奇异连接进行分析，确定其相关的特征电流。其次，哈维和波尔金发展的核的微积分将被用来解决微分几何中的新问题。第三，由Harvey和Lawson引入的校准理论将被应用于几何问题。在实际的几何问题中，区分“局部”信息和“全局”信息是很重要的。这里的“本地”是指某一点的附近，而“全球”则包括诸如从华盛顿特区到地球表面另一个地方的距离等信息。对于应用程序来说，特别重要的结果通常是由局部信息的集合计算全局信息的结果。例如，单独的局部信息，包括表面的局部曲率量，可以用来区分球的全局性质和内胎的全局性质。这项研究将为这一重要程序开发新的实例。

AbstractAward: DMS-9971574Principal Investigator: F. Reese HarveyThis project has three components. First, push forward singularconnections will be analyzed and their associated characteristiccurrents will be determined. Second, the calculus of kernels asdeveloped by Harvey and Polking will be used to attack newproblems in differential geometry. Third, calibration theory,introduced by Harvey and Lawson, will be applied to geometricproblems.In practical geometric problems it is important to distinguish"local" from"global" information. Here "local" means in thevicinity of a point while by contrast "global" includesinformation such as the distance from, say Washington D.C., toanother place on the surface of the earth. Results of particularimportance for applications are frequently ones where globalinformation is computed from an assembly of local information.For example local information alone, involving the amount oflocal curvature of a surface can be used to distinguish theglobal nature of a ball from the global nature of a innertube. This research will develope new instances of this importantprocedure.