Abstract
We consider the long-time behaviour of the mean curvature flow of spacelike hypersurfaces in the Lorentzian product manifold Mtimes mathbb {R}, where M is asymptotically flat. If the initial hypersurface F_0subset Mtimes mathbb {R} is uniformly spacelike and asymptotic to Mtimes left{ sright} for some sin mathbb {R} at infinity, we show that a mean curvature flow starting at F_0 exists for all times and converges uniformly to Mtimes left{ sright} as trightarrow infty .
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