Inverse mean curvature flow with forced term

In this paper, we study the evolution of convex hypersurfaces by inverse mean curvature minus an external force field c. We prove that the flow will preserve the convexity for any c. If c < 1 H on the initial surface, we prove that the flow will expand the hypersurface for all time, and after rescaling the hypersurface will converge to a sphere. If c > 1 H on the initial surface, we show that the maximum existence time of the flow is finite, and the hypersurface will contract to a point when approaching the final time.