Commentarii Mathematici Helvetici


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Volume 72, Issue 1, 1997, pp. 52–66
DOI: 10.1007/PL00000366

Published online: 1997-03-31

Volume-preserving mean curvature flow of rotationally symmetric surfaces

Maria Athanassenas[1]

(1) Monash University, Victoria, Australia

A rotationally symmetric n-dimensional surface in ${\Bbb R}^{n+1}$, 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.

Keywords: Geometric evolution equations, motion by mean curvature under a volume constraint

Athanassenas Maria: Volume-preserving mean curvature flow of rotationally symmetric surfaces. Comment. Math. Helv. 72 (1997), 52-66. doi: 10.1007/PL00000366