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A maximum principle for self-shrinkers and some consequences

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Type
Preprint
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Submission Date
Identifiers
arXiv ID: 1412.4755
Source
arXiv
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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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