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Spacelike hypersurfaces with prescribed mean curvature have played a major role in the study of Lorentzian manifolds Maximal mean curvature zero hypersurfaces were used in the rst proof of the positive mass theorem Constant mean curvature hypersurfaces provide convenient time gauges for the Einstein equations For a survey of results we refer to In and it was shown that entire solutions of the maximal surface equation

Interior estimates and longtime solutions for mean curvature flow of noncompact spacelike hypersurfaces in Minkowski space