Evolution of noncompact hypersurfaces by mean curvature minus a kind of external force field

Abstract

In this paper, we study the evolution of a noncompact hypersurface moving by mean curvature minus an external force field. We prove that the flow has a long-time smooth solution for a kind of special external force fields if the initial hypersurface is a Lipschitz entire graph with linear growth.

Keywords

parabolic equation / mean curvature flow / maximum principle