Abstract.
We study developing singularities for surfaces of rotation with free boundaries and evolving under volume-preserving mean curvature flow. We show that singularities form a finite, discrete set along the axis of rotation. We prove a monotonicity formula and conclude that type I singularities are asymtotically cylindrical.
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Received: 12 January 2000 / Accepted: 23 January 2001 / Published online: 17 December 2002
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Athanassenas, M. Behaviour of singularities of the rotationally symmetric, volume-preserving mean curvature flow. Cal. Var. 17, 1–16 (2003). https://doi.org/10.1007/s00526-002-0098-4
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DOI: https://doi.org/10.1007/s00526-002-0098-4