Geometric Analysis, Applications in the Analysis of Some Applied Math PDE's, and Developing Geometry Courses for Freshmen and Math Education Majors

几何分析、一些应用数学偏微分方程分析中的应用以及为新生和数学教育专业开发几何课程

• 批准号: 9704488
• 负责人: Zheng-Chao Han
• 金额: $ 6.94万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-06-15 至 2001-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704488&HistoricalAwards=false
• 关键词: Geometric; Analysis; Applications; Some; Applied

9704488 Han The project lies in the general area of Riemannian geometry. The investigator is to pursue questions related to scalar and Gauss curvatures, geometric PDEs (vortex sheet equation), and the geometry of harmonic maps into negatively curved surfaces. The project also contains an education component involving the undergraduate geometry curriculum. Geometric partial differential equations use techniques from various areas in geometric analysis such as harmonic maps and Riemannian geometry to solve differential equations arising in a variety of contexts. For example, the vortex sheet equation is related to the evolution of vortices in the air and other fluids as well as to phase transitions in super-conductivity.

9704488 Han该项目属于黎曼几何的一般领域。研究者将研究与标量和高斯曲率、几何偏微分方程（涡片方程）以及调和映射到负曲面的几何相关的问题。该项目还包含了一个涉及本科几何课程的教育部分。几何偏微分方程使用几何分析中各个领域的技术，如谐波映射和黎曼几何来解决在各种情况下出现的微分方程。例如，涡片方程与空气和其他流体中涡的演化以及超导中的相变有关。