ENTIRE DOWNWARD TRANSLATING SOLITONS TO THE MEAN CURVATURE FLOW IN MINKOWSKI SPACE

In this paper, we study entire translating solutions u(x) to a mean curvature flow equation in Minkowski space. We show that if {(x,u(x))vertical bar x is an element of R-n} is a strictly spacelike hypersurface, then Sigma reduces to a strictly convex rank k soliton in R-k,R-1 (after splitting off trivial factors) whose "blowdown" converges to a multiple lambda is an element of (0, 1) of a positively homogeneous degree one convex function in R-k. We also show that there is nonuniqueness as the rotationally symmetric solution may be perturbed to a solution by an arbitrary smooth order one perturbation.