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.

几何谱理论是一个数学领域，位于交叉分析，偏微分方程和微分几何。该提案的重点是拉普拉斯算子和其他微分算子的特征值和特征函数的性质定义的几何对象。大多数问题的动机是源于对真实的生活现象的研究，如膜和板的振动，流体的振荡和量子力学效应。