Mathematical Sciences: Intrinsic and Extrinsic Curvature of Singular Spaces

傅教授将研究奇异空间上标量值曲率的可能类比。首席研究员已经在这个方向上取得了一些进展，并将尝试将他的工作从特殊情况扩展到更一般的奇异空间。研究中使用的主要方法是几何测度论。这项研究的目的之一是了解如何将几何的经典不变量(如曲率)扩展到奇异空间，即具有角、尖点或自交的空间。这些经典不变量对于我们理解空间的几何是非常重要的，将这些概念扩展到奇异空间应该立即有应用，因为奇异空间在物理系统的建模中发挥着越来越重要的作用。

Professor Fu will study possible analogs of scalar-valued curvatures on singular spaces. The principal investigator has already made some progress in this direction and will try to extend his work from special cases to more general singular spaces. The primary method to be used in the investigation is geometric measure theory. One of the goals of this research is to understand how classical invariants of geometry such as curvature can be extended to singular spaces, that is, spaces with corners, cusps, or self intersections. These classical invariants are very important in our understanding of the geometry of a space and the extension of these concepts to singular spaces, which are playing an increasingly central role in the modeling of physical systems, should have immediate application.