Mathematical Sciences: Regularity and Singularity in Geometric Variational and Flow Problems

数学科学：几何变分和流问题中的正则性和奇异性

• 批准号: 9504456
• 负责人: Leon Simon
• 金额: $ 35.15万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504456&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Regularity; Singularity; Geometric

Simon 9504456 Two related topics of research are proposed: singularities of energy minimizing maps and curvature flows. Simon pioneered analytic techniques for studying the top-dimensional singular set of an energy minimizing map, for which he recently won the Bocher prize. In addition to continuing this research - which could lead to a resolution of the important conjecture asserting that minimizers of energy are stratified manifolds - several problems on curvature flows are proposed. Proposed curvature flow problems model a wide range of phenomena, such as the dynamics of soap films, immiscible fluids and crystal growth, and lie in the area of nonlinear parabolic partial differential equations.

Simon 9504456提出了两个相关的研究主题：能量的奇异性最小化图和曲率流。西蒙开创了分析技术，用于研究一组能量最小化的地图，他最近获得了Bocher奖。除了继续进行这项研究之外，还可以解决重要的猜想，认为最小化的能量是分层的歧管 - 提出了曲率流的几个问题。 提出的曲率流问题模拟了广泛的现象，例如肥皂膜的动力学，不混溶的流体和晶体生长，并位于非线性抛物线层状偏微分方程的区域。