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arXiv · 1504.01996

A Topological Property of Asymptotically Conical Self-Shrinkers of Small Entropy

Jacob Bernstein·Lu Wang
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Abstract

For any asymptotically conical self-shrinker with entropy less than or equal to that of a cylinder we show that the link of the asymptotic cone must separate the unit sphere into exactly two connected components, both diffeomorphic to the self-shrinker. Combining this with recent work of Brendle, we conclude that the round sphere uniquely minimizes the entropy among all non-flat two-dimensional self-shrinkers. This confirms a conjecture of Colding-Ilmanen-Minicozzi-White in dimension two.

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Jacob Bernstein, Lu Wang. 2015-04-08. A Topological Property of Asymptotically Conical Self-Shrinkers of Small Entropy. https://doi.org/10.1215/00127094-3715082

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