Mathematical Sciences: Applications of Elliptic PDE's to Geometry and Topology

数学科学：椭圆偏微分方程在几何和拓扑中的应用

• 批准号: 9200576
• 负责人: Edward Miller
• 金额: $ 20.21万
• 依托单位: Polytechnic University of New York
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9200576&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Applications; Elliptic; PDE

The principal investigators will study geometric scale- invariant elliptic partial differential equations. Such equations arise naturally in many fields of mathematics including topology, geometry , and mathematical physics. The three specific areas of research supported by this award are Dirac type operators, Yang- Mills equations, and curvature functionals. 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尺度- 不变椭圆型偏微分方程等 方程自然出现在许多数学领域，包括 拓扑学几何学和数学物理学的三项具体 该奖项支持的研究领域是狄拉克类型的 算子、杨-米尔斯方程和曲率泛函。 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