Mathematical Sciences: Evolution Equations in Geometry

数学科学：几何演化方程

• 批准号: 9504528
• 负责人: Richard Hamilton
• 金额: $ 13.5万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504528&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Evolution; Equations; Geometry

Hamilton 9504528 The proposed research is in the area of nonlinear parabolic partial differential equations - for example, the heat equation - arising in differential geometry and the physical sciences. The proposer has previously obtained a number of results on the quantitative and qualitative aspects of the solutions to these parabolic differential equations; these results, in turn, led to applications in smooth manifold theory. In particular, the proposer's work on the diffeomorphism classification of four-manifolds with positive isotropic curvature is considered an important result in the field. Applications of the proposed research in the physical sciences include movement of solid-liquid interfaces of materials, wear of material bodies under random impart, motion of lubricating fluids, and evolution of liquid crystals.

汉密尔顿9504528 拟议的研究是在非线性抛物型偏微分方程领域-例如，热方程-在微分几何和物理科学中出现。提议者以前已经获得了一些结果的定量和定性方面的解决方案，这些抛物型微分方程，这些结果，反过来，导致应用光滑流形理论。特别是，提议者的工作的同胚分类的四个流形与积极的迷向曲率被认为是一个重要的结果在该领域。 在物理科学中的应用包括材料的固-液界面的运动，在随机影响下的物质体的磨损，润滑流体的运动和液晶的演化。