Mathematical Sciences: Geometric Evolution Equations, Einstein Manifolds, Minimal Surfaces and Pseudo Holomorphic Curves

数学科学：几何演化方程、爱因斯坦流形、最小曲面和伪全纯曲线

• 批准号: 9106760
• 负责人: Rugang Ye
• 金额: --
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-15 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9106760&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Evolution; Equations

Professor Ye will study evolution equations and applications to problems in Riemannian geometry. In particular he will study the Ricci flow, the Yamabe flow, and the harmonic mapping flow. The method of evolution equations has become an important method for finding critical points of geometric functionals and in understanding the dynamic structure of space. The evolution equations to be studied in this research can be understood physically by imagining a stretched rubber band immersed in a viscous fluid such as oil. The evolution equation for this example then describes the way in which the rubber band shrinks. The speed at which it shrinks at any point on the band is proportional to how much the band is curved at that point. Since so many physical problems involve deformation of curves or surfaces, the potential for application of this research is substantial.

叶教授将研究演化方程及其在黎曼几何问题中的应用。他将特别研究 Ricci 流、Yamabe 流和谐波映射流。演化方程方法已成为寻找几何泛函临界点和理解空间动态结构的重要方法。本研究中要研究的演化方程可以通过想象浸入油等粘性流体中的拉伸橡皮筋来物理理解。此示例的演化方程描述了橡皮筋收缩的方式。带子上任何一点的收缩速度与带子在该点的弯曲程度成正比。由于许多物理问题都涉及曲线或曲面的变形，因此这项研究的应用潜力是巨大的。