JournalscmhVol. 72 , No. 1DOI 10.1007/pl00000366

Volume-preserving mean curvature flow of rotationally symmetric surfaces

  • Maria Athanassenas

    Monash University, Victoria, Australia
Volume-preserving mean curvature flow of rotationally symmetric surfaces cover

Abstract

A rotationally symmetric n-dimensional surface in Rn+1{\Bbb 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.