Mathematical Sciences: Geometry and Analysis on Kahler Manifolds

数学科学：卡勒流形的几何与分析

• 批准号: 9504925
• 负责人: Huai-Dong Cao
• 金额: $ 3万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504925&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Analysis; Kahler

9504925 Cao The proposal lies in complex geometry and differential equations, and deals specifically with the Ricci flow - otherwise known as the parabolic Einstein equation, which is a geometric evolution equation - on Kahler manifolds. The main goal is to understand the asymptotic behavior of solutions to the Ricci flow on a compact Kahler manifold of positive holomorphic bisectional curvature. Geometric evolution equations arise in nature. And although the proposed research deals with somewhat technical aspects of a specific geometric evolution equation, it is possible that it will lead to important techniques applicable to a broader class of evolution equations.

9504925 CaO该建议涉及复杂的几何和微分方程式，具体涉及卡勒流形上的Ricci流--也称为抛物型爱因斯坦方程，这是一个几何演化方程。主要目的是了解具有正全纯对分曲率的紧致Kahler流形上的Ricci流解的渐近行为。几何演化方程是自然界中产生的。虽然拟议的研究涉及特定几何演化方程的一些技术方面，但它可能会导致重要的技术适用于更广泛类别的演化方程。