Published September 15, 2015
| Submitted
Journal Article
Open
Universality in mean curvature flow neckpinches
- Creators
- Gang, Zhou
- Knopf, Dan
Chicago
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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.
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.Attached Files
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Additional details
- Eprint ID
- 61487
- DOI
- 10.1215/00127094-3146175
- Resolver ID
- CaltechAUTHORS:20151023-111731559
- NSF
- DMS-1308985
- NSF
- DMS-1205270
- Created
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2015-10-26Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field