Mathematical Sciences: Asymptotic Behavior and the SingularSet of Minimal Surfaces and Harmonic Maps

数学科学：渐近行为以及最小曲面和调和图的奇异集

• 批准号: 9207704
• 负责人: Leon Simon
• 金额: $ 27万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9207704&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Asymptotic; Behavior; SingularSet

The principal investigators will study geometric variational problems and singularities of solutions. Professor Simon will concentrate his research on the structure of the singular set of minimal surfaces and harmonic maps. He will also consider asympotics on approach to singular points including the unique tangent cone problem. Professor White will investigate the bridge theorem for minimal surfaces, branch points in minimal surfaces, uniqueness of tangent cones and tangent maps in minimal varieties and harmonic maps. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.

主要研究人员将研究几何变分 问题和解决方案的奇异性。西蒙教授将 把他的研究集中在奇异集合的结构上， 极小曲面和调和映射。他也会考虑 渐近方法的奇异点，包括唯一的 切锥问题白色教授将调查这座桥 极小曲面定理，极小曲面中的分支点， 极小簇中切锥和切映射的唯一性 和调和映射 该奖项将支持一般领域的研究， 微分几何和全局分析。微分几何 是研究空间的几何形状 和空间上定义的分析概念。全球分析是 对物体的整体几何和拓扑性质的研究 一个空间，通过拼凑当地的信息。的应用 这些数学领域的其他科学包括 复杂的分子结构，液-气边界， 宇宙的大尺度结构