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 Σ = {(x, u(x))∣x ϵ Rⁿ} is a strictly spacelike hypersurface, then Σ reduces to a strictly convex rank k soliton in R^k,1 (after splitting off trivial factors) whose "blowdown" converges to a multiple λ ϵ (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. [ABSTRACT FROM AUTHOR]