Curvature flows and spectral estimates.

曲率流和谱估计。

• 批准号: FT130101102
• 负责人: Dr Julie Clutterbuck
• 金额: $ 41.97万
• 依托单位: Monash University
• 依托单位国家: 澳大利亚
• 项目类别: ARC Future Fellowships
• 财政年份: 2014
• 资助国家: 澳大利亚
• 起止时间: 2014-04-01 至 2021-12-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/FT130101102
• 关键词: Curvature; flows; spectral; estimates.

Curvature flows are a class of geometrically motivated equations, modelled on the heat equation. Recently, researchers have developed new methods for studying the regularity of solutions to these equations, and applied them to a different problem, that of estimating quantities depending on the smaller eigenvalues of a Schroedinger operator. This project builds on the early success of this research and will produce a new understanding of the behaviour of eigenvalues, establish sharp estimates for spectral quantities, particularly on manifolds with curvature bounds, and find optimal conditions under which non-compact solutions to curvature flows are stable.

曲率流是一类几何激励方程，以热方程为模型。最近，研究人员开发了新的方法来研究这些方程的解的正则性，并将其应用于不同的问题，即估计依赖于薛定谔算子的较小本征值的量。该项目建立在这项研究的早期成功，并将产生一个新的理解的行为特征值，建立尖锐的估计谱量，特别是在流形曲率边界，并找到最佳条件下，非紧的解决方案曲率流是稳定的。