Mathematical Sciences: Geometry of the Laplacian

数学科学：拉普拉斯几何

• 批准号: 9200313
• 负责人: Robert Brooks
• 金额: $ 9.5万
• 依托单位: University of Southern California
• 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 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9200313&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Laplacian

The principal investigator will study the relationship between the Laplacian of a compact manifold and the geometry of the manifold. He will attempt to determine the extent to which the spectrum of the manifold determines the class up to finitely many topological types. The principal investigator will also study the relationship between spectrum and other geometric quantities such as diameter and injectivity radius. 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.

主要研究者将研究紧流形的拉普拉斯量与流形几何之间的关系。他将试图确定流形的谱在多大程度上决定了到有限多个拓扑类型的类。首席研究员还将研究光谱与其他几何量（如直径和注入半径）之间的关系。该奖项将支持微分几何和全局分析领域的研究。微分几何是研究空间几何与空间上定义的解析概念之间关系的学科。全局分析是通过拼凑局部信息来研究空间的整体几何和拓扑特性。这些数学领域在其他科学中的应用包括复杂分子的结构、液气边界和宇宙的大尺度结构。