A PINCHING ESTIMATE FOR CONVEX HYPERSURFACES EVOLVING UNDER A NON-HOMOGENEOUS VARIANT OF MEAN CURVATURE FLOW

摘要

We study a variant of the mean curvature flow for closed, convex hypersurfaces where the normal velocity is a non-homogeneous function of the principal curvatures. We show that if the initial hypersurface satisfies a certain pinching condition, then this is preserved and the flow converges to a sphere under rescaling.