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arXiv · 1412.4755

A maximum principle for self-shrinkers and some consequences

Antoine Song
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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.

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Antoine Song. 2014-12-15. A maximum principle for self-shrinkers and some consequences. https://arxiv.org/abs/1412.4755

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