Mathematical Sciences: Geometry of Surfaces, Soliton Equations, and Loop Groups

数学科学：曲面几何、孤子方程和环群

• 批准号: 9205293
• 负责人: Josef Dorfmeister
• 金额: $ 5万
• 依托单位: University of Kansas Main Campus
• 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: 1992-09-15 至 1996-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9205293&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Surfaces; Soliton

The principal investigator will continue his study of minimal surfaces in spaces of constant mean curvature. In particular he will study surfaces of higher genus such as the torus embedded in the sphere. The techniques to be used involve integrable systems in infinite dimensional spaces. This technique is very different from the standard methods used to study these problems thus far. 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.

主要研究者将继续研究常平均曲率空间中的极小曲面。特别是，他将研究更高亏格的曲面，如嵌入球体中的环面。所使用的技术涉及无限维空间中的可积系统。这项技术与迄今用于研究这些问题的标准方法有很大不同。该奖项将支持在微分几何和全球分析的一般领域的研究。微分几何是研究空间几何和定义在该空间上的解析概念之间的关系的学科。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性质的学科。这些领域的数学在其他科学中的应用包括复杂分子结构、液体-气体边界和宇宙的大尺度结构。