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。在很大程度上，它是由源于现实生活现象的研究的问题，例如振动，热传播，流体的振荡和量子机械效应。该提案的第一部分与Steklov问题的光谱几何形状有关。 V. Steklov于1902年引入的这个特征值问题具有许多重要的应用，但纯粹的数学家仍然相对尚未探索。拟议的研究主题包括研究奇异的steklov型问题，例如荡妇问题。 等光谱和光谱不变； steklov特征函数的淋巴结几何形状。该提案的第二部分重点是在Laplace和Schrodinger操作员的光谱渐近学研究中引起的一些问题。 * * * *