Stability and instability of Einstein manifolds with prescribed asymptotic geometry

具有规定渐近几何的爱因斯坦流形的稳定性和不稳定性

• 批准号: 339994672
• 负责人: Professor Dr. Klaus Kröncke
• 金额: --
• 依托单位: Department of Mathematics
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2017
• 资助国家: 德国
• 起止时间: 2016-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/339994672?language=en
• 关键词: Stability; instability; Einstein; manifolds; prescribed

The general aim of the project is a better understanding of the connection between linear stability, integrability and dynamical stability of noncompact Einstein manifolds as stationary points of the Ricci flow.Within this project, these connections should be studied in particular for Ricci-flat manifolds with prescribed asymptotics. Interesting asymptotics are ALE (asymptotically locally euclidean), ALF, ALG, ALH, asymptotically conical and asymptotic to products of euclidean space with compact Ricci-flat manifolds.In the long-term, these connections shall also be studied for Ricci-flat cone manifolds.

该项目的总体目标是更好地理解作为Ricci流的驻点的非紧Einstein流形的线性稳定性、可积性和动力学稳定性之间的联系。在该项目中，这些联系应特别针对具有规定渐近性的Ricci平坦流形进行研究。有趣的渐近性是ALE（asymptotically locally euclidean），ALF，ALG，ALH，渐近锥，渐近于欧氏空间与紧Ricci-平坦流形的乘积，这些联系在Ricci-平坦锥流形中也将被研究.