  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 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.
