Mathematical Sciences: Geometric Variational Problems and Related PDE Questions

数学科学：几何变分问题及相关偏微分方程问题

• 批准号: 9012718
• 负责人: Leon Simon
• 金额: $ 13.62万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9012718&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Variational; Problems

Two investigators will analyze problems arising from the study of geometric partial differential equations. One will study questions related to asymptotics for geometric extrema, including questions about growth properties of entire solutions of the minimal surface equation and more general quasilinear elliptic equations. He will also work toward a solution of the long-standing Willmore conjecture. The second investigator will study the structure of singular sets of minimal surfaces, asymptotic behavior of harmonic maps near singularities, and topological types of minimal submanifolds. Both investigators will analyze problems which involve understanding how partial differential equations act on minimal surfaces. These equations include derivatives of functions of more than one variable and frequently have their origins in applied mathematics. Minimal surfaces are the mathematician's model of common soap films. In recent years the use of partial differential equations in connection with minimal surfaces has seen an explosion of research activity.

两名调查人员将分析 研究几何偏微分方程。 人会 研究与几何极值的渐近性有关的问题， 包括关于整体解的增长性质的问题 最小曲面方程和更一般的拟线性 椭圆方程 他还将致力于解决 长期存在的Willmore猜想 第二名调查员将 研究极小曲面的奇异集的结构， 调和映射在奇点附近的渐近行为， 极小子流形的拓扑类型 两位研究人员将分析涉及以下问题的问题： 了解偏微分方程如何作用于最小 表面。 这些方程包括以下函数的导数： 一个以上的变量，经常有他们的起源， 应用数学 最小曲面是数学家 普通肥皂膜的模型。 近年来，部分 与极小曲面有关的微分方程 看到了研究活动的爆炸式增长。