Stability and instability of Einstein manifolds with prescribed asymptotic geometry

• Applicant: Professor Dr. Klaus Kröncke
• Subject Area: Mathematics
• Term: from 2017 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 339994672

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.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2026: Geometry at Infinity