Event time:
Friday, February 4, 2022 - 2:00pm
Speaker:
Klaus Kroencke
Speaker affiliation:
Universitat Hamburg
Event description:
Abstract:
We prove stability of integrable ALE manifolds with a parallel spinor under Ricci flow, given an initial metric which is close in Lp∩L∞, for any p∈(1,n), where n is the dimension of the manifold. In particular, our result applies to all known examples of 4-dimensional gravitational instantons. The result is obtained by a fixed point argument, based on novel estimates for the heat kernel of the Lichnerowicz Laplacian. It allows us to give a precise description of the convergence behaviour of the Ricci flow. Our decay rates are strong enough to prove positive scalar curvature rigidity in Lp, for each p∈[1,nn−2), generalizing a result by Appleton. This is joint work with Oliver Lindblad Petersen.