Published September 15, 2015 | Version Submitted
Journal Article Open

Universality in mean curvature flow neckpinches

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.

Additional Information

© 2015 Duke University Press. Received 18 November 2013. Revision received 21 October 2014. The authors are deeply grateful to I. M. Sigal for many helpful discussions related to extensions of their work in [13]. Gang's work was partially supported by National Science Foundation grant DMS-1308985, and Knopf's work was partially supported by National Science Foundation grant DMS-1205270.

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Additional details

Identifiers

Eprint ID
61487
DOI
10.1215/00127094-3146175
Resolver ID
CaltechAUTHORS:20151023-111731559

Related works

Funding

NSF
DMS-1308985
NSF
DMS-1205270

Dates

Created
2015-10-26
Created from EPrint's datestamp field
Updated
2021-11-10
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