ON MEAN-CURVATURE FLOW OF SPACELIKE HYPERSURFACES IN ASYMPTOTICALLY FLAT SPACETIMES

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