géométrie et théorie spectrale

几何与光谱理论

• 批准号: 1000229993-2013
• 负责人: Polterovich, Iosif
• 金额: $ 7.29万
• 依托单位: Université de Montréal
• 依托单位国家: 加拿大
• 项目类别: Canada Research Chairs
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=662403
• 关键词: om; trie; et; th; orie

Geometric spectral theory is an area of mathematics that lies at the intersection of analysis, partial differential equations and differential geometry. To a large extent, it is motivated by questions originating in the study of real life phenomena, such as vibration, heat propagation, oscillations of fluids and quantum mechanical effects. The first part of the proposal is concerned with the spectral geometry of the Steklov problem. This eigenvalue problem, introduced by V. Steklov in 1902, has many important applications, but is still relatively unexplored by pure mathematicians. The proposed topics of research include the study of singular Steklov type problems, such as the sloshing problem; isospectrality and spectral invariants; nodal geometry of Steklov eigenfunctions. The second part of the proposal focuses on some questions arising in the study of spectral asymptotics of Laplace and Schrodinger operators.* *

几何谱理论是一个数学领域，位于分析、偏微分方程和微分几何的交叉点。在很大程度上，它是由源于现实生活现象研究的问题所激发的，例如振动、热传播、流体振荡和量子力学效应。该提案的第一部分涉及 Steklov 问题的谱几何。这个特征值问题由 V. Steklov 于 1902 年提出，具有许多重要的应用，但纯数学家相对而言尚未对其进行探索。拟议的研究主题包括奇异Steklov类型问题的研究，例如晃动问题； 同光谱性和光谱不变量； Steklov 特征函数的节点几何。该提案的第二部分重点讨论拉普拉斯和薛定谔算子谱渐近研究中出现的一些问题。* *