Mathematical Sciences: Evolution Equations in Geometry

数学科学：几何演化方程

• 批准号: 9204336
• 负责人: Richard Hamilton
• 金额: $ 17.87万
• 依托单位: University of California-San Diego
• 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 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9204336&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Evolution; Equations; Geometry

The principal investigator will study evolution equations in differential geometry. In particular he will study the Ricci flow and Yamabe flow. Singularities in the solutions of the flow problems will be one of the main focal points of the research. The principal investigator will try to use blow up methods to study these singularities. 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.

首席研究员将研究进化方程， 微分几何特别是他将研究利玛窦流 山边流流动解的奇异性 问题将是研究的重点之一。 主要研究者将尝试使用放大方法， 研究这些奇异点。 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