Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow

Details Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow

2011-09-05

arxiv.org/abs/1109.0939v1

Mathematics

Differential Geometry

Scientific paper

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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