JournalscmhVol. 72, No. 1pp. 52–66

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
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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.

Cite this article

Maria Athanassenas, Volume-preserving mean curvature flow of rotationally symmetric surfaces. Comment. Math. Helv. 72 (1997), no. 1, pp. 52–66

DOI 10.1007/PL00000366