Published May 2018
| Submitted
Journal Article
Open
Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow
- Creators
- Gang, Zhou
- Knopf, Dan
- Sigal, Israel Michael
Abstract
We study noncompact 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.
Additional Information
© 2018 by the American Mathematical Society. Received by the editor March 29, 2012 and, in revised form, October 4, 2013 and November 20, 2015. Article electronically published on March 29, 2018. The first author thanks NSF for supports in DMS-1308985. The second author thanks NSF for support in DMS-0545984. The third author thanks NSERC for support in NA7901.Attached Files
Submitted - 1109.0939
Files
Files
(759.8 kB)
| Name | Size | Download all |
|---|---|---|
|
md5:1631da24e7ea22d3adfe29ff93a52519
|
759.8 kB | Download |
Additional details
- Eprint ID
- 87576
- Resolver ID
- CaltechAUTHORS:20180705-160626089
- DMS-1308985
- NSF
- DMS-0545984
- NSF
- NA7901
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- Created
-
2018-07-06Created from EPrint's datestamp field
- Updated
-
2021-11-15Created from EPrint's last_modified field