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15 September 2015 Universality in mean curvature flow neckpinches
Zhou Gang, Dan Knopf
Duke Math. J. 164(12): 2341-2406 (15 September 2015). DOI: 10.1215/00127094-3146175

Abstract

We study noncompact surfaces evolving by mean curvature flow. Without any symmetry assumptions, we prove that any solution that is C3-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. "Universality in mean curvature flow neckpinches." Duke Math. J. 164 (12) 2341 - 2406, 15 September 2015. https://doi.org/10.1215/00127094-3146175

Information

Received: 18 November 2013; Revised: 21 October 2014; Published: 15 September 2015
First available in Project Euclid: 16 September 2015

zbMATH: 1329.53093
MathSciNet: MR3397388
Digital Object Identifier: 10.1215/00127094-3146175

Subjects:
Primary: 53C44
Secondary: 35K93

Rights: Copyright © 2015 Duke University Press

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Vol.164 • No. 12 • 15 September 2015
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