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arXiv · 1308.5600

Universality in mean curvature flow neckpinches

Zhou Gang·Dan Knopf
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Abstract

We study noncompact surfaces evolving by mean curvature flow. Without any symmetry assumptions, we prove that any solution that is $C^3$-close at some time to a standard neck will develop a neckpinch singularity in finite time, will become asymptotically rotationally symmetric in a space-time neighborhood of its singular set, and will have a unique tangent flow.

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Zhou Gang, Dan Knopf. 2013-08-26. Universality in mean curvature flow neckpinches. https://doi.org/10.1215/00127094-3146175

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