Rigidity of initial data sets in Minkowski space

16.05.2024, 16:15  –  Raum 1.10
Forschungsseminar Differentialgeometrie

Christian Bär (UP)

If M is a spacelike hypersurface of a Lorentzian manifold, then M inherits an induced Riemannian metric g and a second fundamental form q. The triple (M,g,q) is then called the induced initial data set. It satisfies the Gauss and Codazzi-Mainardi equations.

Now suppose a spin manifold M (with boundary) with Riemannian metric g and (0,2)-tensor q is given. We assume that the dominant energy condition and a similar condition on the mean curvature of the boundary holds. We then show that (M,g,q) is (locally) induced from Minkowski space.

The talk is based on joint work with Simon Brendle, Aaron Chow, and Bernhard Hanke.