A rotationally symmetric n-dimensional surface in , 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.
Cite this article
Maria Athanassenas, Volume-preserving mean curvature flow of rotationally symmetric surfaces. Comment. Math. Helv. 72 (1997), no. 1, pp. 52–66DOI 10.1007/PL00000366