Geometric evolution equations and global effects of curvature

几何演化方程和曲率的全局效应

• 批准号: ARC : DP0344221
• 负责人: Dr Benjamin Andrews
• 金额: $ 40万
• 依托单位: Australian National University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2003
• 资助国家: 澳大利亚
• 起止时间: 2003-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://researchdata.edu.au/geometric-evolution-equations-effects-curvature/62885
• 关键词: Geometric; evolution; equations; global; effects

Geometric evolution equations and global effects of curvature. This project aims to approach several important problems in global differential geometry, by inventing new processes to deform geometric objects to simpler ones. The deformations are described by carefully constructed geometric evolution equations, designed to exhibit behaviour suited to the given problem. The project proposes methods for building such equations, and new techniques for their analysis. The research is expected to yield significant new results, both in differential geometry and in nonlinear heat equations, and should provide substantial progress towards resolving several important long-standing conjectures. \r\n

几何演化方程和曲率的全局效应。该项目旨在通过发明新的过程将几何对象变形为更简单的对象，来解决全局微分几何中的几个重要问题。变形由精心构建的几何演化方程描述，旨在展示适合给定问题的行为。该项目提出了建立这类方程的方法，以及分析它们的新技术。这项研究有望在微分几何和非线性热方程方面产生重要的新结果，并在解决几个重要的长期猜想方面取得实质性进展。\ r \ n