Area-preserving mean curvature flow of rotationally symmetric hypersurfaces with free boundaries

Abstract

We consider the area-preserving mean curvature flow with free Neumann boundaries. We show that for a rotationally symmetric n-dimensional hypersurface in ℝ n+1 between two parallel hyperplanes will converge to a cylinder with the same area under this flow. We use the geometric properties and the maximal principle to obtain gradient and curvature estimates, leading to long-time existence of the flow and convergence to a constant mean curvature surface.