J Austral Math Soc Ser A 55 pp41--59, 1993.

On Mean Curvature Flow of Spacelike Hypersurfaces in Asymptotically Flat Spacetimes

Klaus Ecker

Abstract

We prove a priori estimates for the gradient and curvature of spacelike hypersurfaces moving by mean curvature in a Lorentzian manifold. These estimates are obtained under much weaker conditions than have been previously assumed. We also use mean curvature flow in the construction of maximal slices in asymptotically flat spacetimes. An essential tool is a maximum principle for sub-solutions of a parabolic operator on complete Riemannian manifolds with time-dependent metric.

1991 AMS Subject Classification: 58D25, 83C99, 35K55

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Authors

Klaus Ecker

Department of Mathematics, The University of Melbourne, Parkville, Victoria 3052, Australia.

mailto:ecker@mundoe.maths.mu.oz.au