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

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.

25 pages, 1 figure. Added figure

References in corpus (1)

• Halfspace type Theorems for Self-Shrinkers

Cited by in corpus (18)

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