Local and global scalar curvature rigidity of Einstein manifolds

14.12. bis 14.12.2021, 12:15-13:45  –  room C9A03 Tübingen, room Potsdam Golm
Geometric Analysis, Differential Geometry and Relativity

Klaus Kröncke

An Einstein manifold is called scalar curvature rigid if there are no compactly supported volume-preserving deformation of the metric which increase the scalar curvature. We give various characterizations of scalar curvature rigidity for open Einstein manifolds as well as for closed Einstein manifolds. As an application, we construct mass-decreasing perturbations of the Riemannian Schwarzschild metric and the Taub-Bolt metric. This is joint work with Mattias Dahl

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