Members & Guests

JProf. Dr. Klaus Kröncke

Project leader


Universität Hamburg

E-mail: klaus.kroencke(at)uni-hamburg.de
Telephone: +49 40 42838-5183
Homepage: https://www.math.uni-hamburg.de/home/kro...

Publications within SPP2026

In this paper we establish stability of the Ricci de Turck flow near Ricci-flat metrics with isolated conical singularities. More precisely, we construct a Ricci de Turck flow which starts sufficiently close to a Ricci-flat metric with isolated conical singularities and converges to a singular Ricci-flat metric under an assumption of integrability, linear and tangential stability. We provide a characterization of conical singularities satisfying tangential stability and discuss examples where the integrability condition is satisfied.

 

Related project(s):
21Stability and instability of Einstein manifolds with prescribed asymptotic geometry23Spectral geometry, index theory and geometric flows on singular spaces

We prove that if an ALE Ricci-flat manifold (M,g) is linearly stable and integrable, it is dynamically stable under Ricci flow, i.e. any Ricci flow starting close to g exists for all time and converges modulo diffeomorphism to an ALE Ricci-flat metric close to g. By adapting Tian's approach in the closed case, we show that integrability holds for ALE Calabi-Yau manifolds which implies that they are dynamically stable.

 

Related project(s):
21Stability and instability of Einstein manifolds with prescribed asymptotic geometry

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