Mathematical Sciences: Four Projects in Geometric Analysis

这项拨款支持一项几何学研究计划， 主要研究人员在接下来的时间里进行的分析 两年 该提案包括四个项目。 (1)奇异 解析偏微分方程中的现象;（2） 洛伦兹几何;（3）与高斯映射有关的几何;（4） Grassman流形与凸性理论 的每一个中 项目，调查将从已知的特别 案例到更一般的情况。 一些共同的主题 这些项目是各种概念中的相互关系， 高斯地图 有些课题还处于早期探索阶段 阶段 几何分析的研究是非常重要的 我们对物理世界的理解和模型描述 偏微分方程

This grant supports a program of research in geometric analysis undertaken by the principal investigators over the next two years. The proposal consists of four projects. (1) Singular phenomena in analytic partial differential equations; (2) Lorentzian geometry; (3) Geometry related to the Gauss map; (4) Grassman manifolds and Convexity theory. In each of the projects, the investigations will proceed from known special cases to more general situations. Common themes for some of these projects are the interrelationships in the various notions of Gauss maps. Some of the topics are in early exploratory stage. Studies in geometric analysis are of fundamental importance to our understanding of the physical world and models described by partial differential equations.