Klaus Kröncke: Local and global scalar curvature rigidity of Einstein manifolds

An Einstein manifold (M, g) is called scalar curvature rigid if there is no compactly supported
volume-preserving deformation of the metric g which increases the scalar curvature. We give
various characterizations of scalar curvature rigidity for open precompact Einstein manifolds
as well as for closed Einstein manifolds. As an application, we construct perturbations of the
Riemannian Schwarzschild metric and the Taub-Bolt metric which preserve the length of the
circle at infinity but decrease the mass. This is joint work with Mattias Dahl.