Stability and instability of Einstein manifolds with prescribed asymptotic geometry

该项目的总体目标是更好地理解作为Ricci流稳定点的非紧致爱因斯坦流形的线性稳定性、可积性和动态稳定性之间的联系。在这个项目中，这些联系应该特别研究具有规定渐近的Ricci-flat流形。有趣的渐近性有ALE（渐近局部欧几里得）、ALF、ALG、ALH、渐近圆锥和渐近欧几里得空间与紧致ricci -平坦流形的乘积。从长远来看，这些连接也应该研究里奇扁锥流形。

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.