Rigidity results for mean curvature flow graphical translators moving in non-graphical direction

Abstract

In this paper, we study the rigidity results of complete graphical translating hypersurfaces when the translating direction is not in the graphical direction. We proved that any entire graphical translating surface in the translating direction not parallel to the graphical one is flat if either the translating surface is mean convex or the entropy of the translating surface is smaller than $2$. For higher dimensional case, we show that the same conclusion holds if the graphical translating hypersurface satisfies certain growth condition.