Mathematical Sciences: Mean Curvature Problems in Euclidean Space and Topics in Geometric Analysis

数学科学：欧几里得空间中的平均曲率问题和几何分析主题

• 批准号: 9208666
• 负责人: Nicholas Korevaar
• 金额: $ 6万
• 依托单位: University of Utah
• 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: 1992-12-01 至 1997-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9208666&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Mean; Curvature; Problems

Professor Korevaar will continue to apply previously developed analytic and topological techniques to the geometric structure of constant mean curvature surfaces. Further applications will be made to the study of constant scalar curvature metrics with conformality. resolving these problems is expected to lead to a number of interesting breakthroughs in classical surface theory where previously applied methods were not always successful. Another problem is to continue the manifold decomposition methods developed via spectral theory of the Laplace operator to investigate `shape' phenomena. The PI is also committed to training several graduate students in this area of research.

Korevaar教授将继续申请以前 发展了分析和拓扑技术的几何 常平均曲率曲面结构 进一步 将应用于常数标量的研究 曲率度量与保形性。解决这些 预计问题将导致一些有趣的问题 经典表面理论的突破， 应用的方法并不总是成功的。另一个问题 是继续发展流形分解方法 通过对拉普拉斯算子的谱理论进行研究 “形”的现象。 PI还致力于培训几名 研究生在这方面的研究。