Evolution of convex hypersurfaces by a fully nonlinear flow

In this paper, we study the evolution of convex hypersurfaces by a fully nonlinear function of curvature minus an external force field cc. We prove that the flow will preserve the convexity for any cc. When cnc and minimum of the support function ss satisfies smin>nc, then after a scaling the hypersurface will converge to a sphere. If c>gc>g on the initial surface M0M0 and the diameter of M0M0 satisfies diam(M0)<2nc, we show that the maximal existence time of the flow is finite.