Mean Curvature Flow in Asymptotically Flat Product Spacetimes

We consider the long-time behaviour of the mean curvature flow of spacelike hypersurfaces in the Lorentzian product manifold M × R , where M is asymptotically flat. If the initial hypersurface F 0 ⊂ M × R is uniformly spacelike and asymptotic to M × s for some s ∈ R at infinity, we show that a mean curvature flow starting at F 0 exists for all times and converges uniformly to M × s as t → ∞ .