Volume comparison for $C^{1,1}$ metrics

Melanie Graf

Published 2015-07-31Version 1

We establish volume comparison results for balls in Riemannian manifolds with $C^{1,1}$-metrics with a lower bound on the Ricci tensor and for the evolution of spacelike, acausal, causally complete hypersurfaces with an upper bound on the mean curvature in spacetimes (Lorentzian manifolds with time orientation) with $C^{1,1}$-metrics with a lower bound on the timelike Ricci curvature. These results are then used to give proofs of Myers' theorem and of Hawking's singularity theorem in this regularity.