Stability of non-compact manifolds under curvature flows

曲率流下非紧流形的稳定性

• 批准号: 42840189
• 负责人: Professor Dr. Oliver Schnürer
• 金额: --
• 依托单位: Mathematics Institute
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2007
• 资助国家: 德国
• 起止时间: 2006-12-31 至 2009-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/42840189?language=en
• 关键词: Stability; non; compact; manifolds; under

In this project, we study the evolution of non-compact manifolds under geometric flows like mean curvature flow or Ricci flow. We are particularly interested in the long-time behavior of solutions which are initially close to a soliton at spatial infinity. We want to study, whether these solutions converge for large times to that soliton. One of the motivations for this project is that we want to understand the long-time dynamical behavior of these flows near eternal solutions. We expect that our investigations will involve methods based on barrier techniques and on considering entropies in integral form.

在这个项目中，我们研究了平均曲率流或里奇流等几何流下非紧流形的演化。我们对最初接近空间无限处的孤子的解的长期行为特别感兴趣。我们想要研究这些解是否多次收敛于该孤子。该项目的动机之一是我们希望了解这些流接近永恒解的长期动态行为。我们期望我们的研究将涉及基于势垒技术和考虑积分形式的熵的方法。