Regulary and stability of curvature flows and their applications to geometric variational problems

曲率流的规律性和稳定性及其在几何变分问题中的应用

• 批准号: 62175069
• 负责人: Professor Dr. Felix Schulze
• 金额: --
• 依托单位: Mathematics Institute
• 依托单位国家: 德国
• 项目类别: Independent Junior Research Groups
• 财政年份: 2007
• 资助国家: 德国
• 起止时间: 2006-12-31 至 2013-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/62175069?language=en
• 关键词: Regulary; stability; curvature; flows; their

In this project we study regularity and stability properties of curvature flows and their applications to geometric variational problems. We are especially interested in the regularity theory for weak mean curvature flow in the formulation of the level-set-flow or Brakke-flow. We also want to study the dynamic stability of non-compact manifolds under curvature flows like mean curvature flow and Ricci flow. We hope to understand the long-time behavior of these flows near eternal solutions. Furthermore we aim at applying curvature flows of this type to geometric variational problems like isoperimetric inequalities and foliations of asymptotically flat space-times.

在这个项目中，我们研究曲率流的规律性和稳定性特性及其在几何变分问题中的应用。我们对水平集流或布拉克流公式中弱平均曲率流的正则理论特别感兴趣。我们还想研究非紧流形在曲率流（如平均曲率流和 Ricci 流）下的动态稳定性。我们希望了解这些流的长期行为接近永恒的解决方案。此外，我们的目标是将这种类型的曲率流应用于几何变分问题，例如等周不等式和渐近平坦时空的叶状结构。

项目成果

Uniqueness of compact tangent flows in Mean Curvature Flow

平均曲率流中紧凑切线流的独特性

• DOI: 10.1515/crelle-2012-0070
• 发表时间: 2014
• 期刊: arXiv: Differential Geometry
• 作者: F. Schulze