Canonical metrics and geometric flows on non-compact manifolds

非紧流形上的规范度量和几何流

• 批准号: 327637-2011
• 负责人: Chau, Albert
• 金额: $ 0.95万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=527045
• 关键词: Canonical; metrics; geometric; flows; non

Differential geometry is the study of space, its shape, and the interaction between the two. My research focuses in two categories of this study. The first category involves studying the underlying fabric of space itself and how this is influenced by its shape. Conversely, we also study the problem of determining when an underlying space can assume certain ideal shapes corresponding to geometric objects with beautiful mathematical descriptions, but for which concrete examples are very hard to construct. The second category involves studying ways in which subspaces move within a larger space. The main analytic tools I use to study problems in these two categories are the Ricci flow equation and the mean curvature flow equation respectively. The Ricci flow equation essentially prescribes a way to deform the shape of any given space into a geometrically nicer one. The remarkable thing is that in many cases, the flow actually produces

微分几何是对空间、空间形状以及两者之间相互作用的研究。 我的研究重点是本研究的两个类别。 第一类涉及研究空间本身的底层结构以及其形状如何影响它。 相反，我们还研究确定底层空间何时可以呈现与具有美丽数学描述的几何对象相对应的某些理想形状的问题，但具体的例子很难构建。 第二类涉及研究子空间在较大空间内移动的方式。 我用来研究这两类问题的主要分析工具分别是里奇流方程和平均曲率流方程。 里奇流方程本质上规定了一种将任何给定空间的形状变形为几何上更好的形状的方法。值得注意的是，在许多情况下，流程实际上会产生