Volume-preserving mean curvature flow of rotationally symmetric surfaces

Abstract

A rotationally symmetric n-dimensional surface in ${\mathbb{R}}^{n+1}$, of enclosed volume V and with boundary in two parallel planes, is evolving under volume-preserving mean curvature flow. For large volume V, we obtain gradient and curvature estimates, leading to long-time existence of the flow, and convergence to a constant mean curvature surface.