Geometric analysis on non-compact and singular spaces

非紧奇异空间的几何分析

• 批准号: 356266-2013
• 负责人: Rochon, Frédéric
• 金额: $ 1.09万
• 依托单位: Université du Québec à Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=595798
• 关键词: Geometric; analysis; non; compact; singular

Geometric analysis is about the study of partial differential equations in geometric settings. On one hand, one can study differential equations like the wave equation or the heat equation on curved spaces and look how the geometry and the topology influence the solutions to these equations. On the other hand, geometric analysis also plays an important role in the solutions of certain geometric problems, typically the search on a given space of a Riemannian metric (a geometry) with nice properties like a uniform curvature. Indeed, quite often, one obtains such metrics by solving a partial differential equation, for instance one can think of Einstein's equation in the theory of general relativity.

几何分析是对几何条件下偏微分方程的研究。一方面，人们可以研究波动方程或热方程等微分方程在弯曲空间上，并观察几何和拓扑结构如何影响这些方程的解。另一方面，几何分析在某些几何问题的解中也起着重要的作用，典型的是在给定空间上搜索具有均匀曲率等良好性质的黎曼度量（一种几何）。事实上，很多时候，人们通过求解偏微分方程得到这样的度规，例如，人们可以想到广义相对论中的爱因斯坦方程。