Curvature flow with a general forcing term in Euclidean spaces

We consider closed convex hypersurfaces moving in Euclidean spaces with normal velocity equal to h−F, where h=h(t) is a nonnegative continuous function of t and F is evaluated at the principal curvatures and satisfies the standard conditions. We study long time existence and convergence of the evolving hypersurfaces in three different cases, which include Andrews' contractive case, McCoy's mixed volume preserving case and the additional expanding case.