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arXiv · 1507.08931

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

Melanie Graf
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Abstract

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.

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Melanie Graf. 2015-07-31. Volume comparison for $C^{1,1}$ metrics. https://doi.org/10.1007/s10455-016-9508-2

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