Mean curvature flow and Ricci flow

平均曲率流和里奇流

• 批准号: RGPIN-2016-04331
• 负责人: Haslhofer, Robert
• 金额: $ 1.97万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635309
• 关键词: Mean; curvature; flow; Ricci

The proposed research is at the intersection of differential geometry, partial differential equations, calculus of variations, stochastic analysis and general relativity. Specifically, the main focus is on two geometric versions of the heat equation: the evolution of surfaces by their mean curvature, and the evolution of curved spaces by Hamilton’s Ricci flow. Mean curvature flow models many physical processes which involve an evolving surface, or interface. It is the most efficient way to decrease the area of surfaces and to evolve them towards optimal ones. Correspondingly, Ricci flow deforms curved spaces towards optimal shapes.

拟议的研究是在微分几何，偏微分方程，变分法，随机分析和广义相对论的交叉点。具体来说，主要的重点是两个几何版本的热方程：表面的演变，其平均曲率，和演变的弯曲空间的汉密尔顿的里奇流。平均曲率流模拟了许多物理过程，这些过程涉及到一个不断变化的表面或界面。这是最有效的方法来减少表面的面积，并向最佳的发展。相应地，Ricci流使弯曲空间朝向最佳形状变形。