Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow

arxiv: 1109.0939 · v2 · pith:HMLUGDU5new · submitted 2011-09-05 · 🧮 math.DG · math.AP

Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow

Zhou Gang , Dan Knopf , Israel Michael Sigal This is my paper

classification 🧮 math.DG math.AP

keywords curvaturemeanbecomeevolvingflowneckpinchsingularitysolutions

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We study surfaces evolving by mean curvature flow (MCF). For an open set of initial data that are $C^3$-close to round, but without assuming rotational symmetry or positive mean curvature, we show that MCF solutions become singular in finite time by forming neckpinches, and we obtain detailed asymptotics of that singularity formation. Our results show in a precise way that MCF solutions become asymptotically rotationally symmetric near a neckpinch singularity.

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Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow

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