Published October 26, 2022
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A maximum principle for self-shrinkers and some consequences
- Creators
- Song, Antoine
Abstract
Using a maximum principle for self-shrinkers of the mean curvature flow, we give new proofs of a rigidity theorem for rotationally symmetric compact self-shrinkers and a result about the asymptotic behavior of self-shrinkers. This comparison argument also implies a linear bound for the second fundamental form of self-shrinking surfaces under natural assumptions. As a consequence, translating solitons can be related to these self-shrinkers.
Additional Information
I would like to thank Niels Møller for proofreading a preliminary version of this note and for his numerous suggestions. I also wish to thank my professors Fernando C. Marques, Olivier Biquard and Laurent Hauswirth for their guidance.Additional details
- Eprint ID
- 117602
- Resolver ID
- CaltechAUTHORS:20221026-539161000.17
- Created
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2022-10-26Created from EPrint's datestamp field
- Updated
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2022-10-26Created from EPrint's last_modified field