Topics in geometric spectral theory

几何谱理论主题

• 批准号: 261570-2012
• 负责人: Polterovich, Iosif
• 金额: $ 2.55万
• 依托单位: Université de 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=594605
• 关键词: Topics; geometric; spectral; theory

Geometric spectral theory is an area of mathematics that lies at the intersection of analysis, partial differential equations and differential geometry. The proposal focuses on the properties of eigenvalues and eigenfunctions of the Laplacian and other differential operators defined on geometric objects. Most problems are motivated by questions originating in the study of real life phenomena, such as vibration of membranes and plates, oscillations of fluids and quantum-mechanical effects.

几何光谱理论是数学领域，位于分析，部分微分方程和差异几何形状的交集。该提案重点介绍了在几何对象上定义的Laplacian和其他差分运算符的特征值和特征函数的特性。大多数问题是由源自研究现实现象的研究的问题，例如膜和板的振动，流体的振荡和量子力学效应。