Geometry of Surfaces, Soliton Equations and Loop Groups

曲面几何、孤子方程和环群

• 批准号: 9705479
• 负责人: Josef Dorfmeister
• 金额: $ 15万
• 依托单位: University of Kansas Main Campus
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-05-15 至 2001-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9705479&HistoricalAwards=false
• 关键词: Geometry; Surfaces; Soliton; Equations; Loop

9705479 Dorfmeister This project lies in the area of minimal surfaces and harmonic mappings. Earlier, the investigator has developed a Weierstrass type formula for harmonic maps from Riemann surfaces into compact symmetric spaces. The current project is a continuation of that work. In particular, the method is to be applied to produce constant mean curvature surfaces in 3-space. Minimal surfaces and constant mean curvature surfaces have certain optimizing properties; as a consequence, they have important physical applications. For example, the interface of two homogeneous media often forms a minimal surface as such a surface tends to be locally energy-minimizing. Constant mean curvature surfaces arise as closed surfaces that have the least surface area amongst all closed surfaces enclosing a fixed volume.

9705479 Dorfmeister这个项目属于最小曲面和谐波映射的领域。早些时候，研究者已经开发了从黎曼曲面到紧致对称空间的调和映射的Weierstrass型公式。目前的项目是这项工作的延续。特别地，该方法应用于三维空间中产生常平均曲率曲面。最小曲面和等平均曲率曲面具有一定的优化性质；因此，它们具有重要的物理应用。例如，两种均质介质的界面往往形成一个最小表面，因为这样的表面往往是局部能量最小的。常平均曲率曲面作为封闭曲面出现，在所有封闭曲面中具有最小的表面积，包围着一个固定的体积。