Volume-preserving flow by powers of the m-th mean curvature

Abstract

We consider the evolution of a closed convex hypersurface under a volume preserving curvature flow. The speed is given by a power of the m-th mean curvature plus a volume preserving term, including the case of powers of the mean curvature or of the Gauss curvature. We prove that if the initial hypersurface satisfies a suitable pinching condition, the solution exists for all times and converges to a round sphere.

Cited by in corpus (1)

• Convex hypersurfaces with pinched principal curvatures and flow of convex hypersurfaces by high powers of curvature