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15 February 2017 A topological property of asymptotically conical self-shrinkers of small entropy
Jacob Bernstein, Lu Wang
Duke Math. J. 166(3): 403-435 (15 February 2017). DOI: 10.1215/00127094-3715082

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 nonflat two-dimensional self-shrinkers. This confirms a conjecture of Colding, Ilmanen, Minicozzi, and White in dimension two.

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Jacob Bernstein. Lu Wang. "A topological property of asymptotically conical self-shrinkers of small entropy." Duke Math. J. 166 (3) 403 - 435, 15 February 2017. https://doi.org/10.1215/00127094-3715082

Information

Received: 30 April 2015; Revised: 18 March 2016; Published: 15 February 2017
First available in Project Euclid: 14 October 2016

zbMATH: 1380.53069
MathSciNet: MR3606722
Digital Object Identifier: 10.1215/00127094-3715082

Subjects:
Primary: 53C44
Secondary: 35K55

Rights: Copyright © 2017 Duke University Press

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Vol.166 • No. 3 • 15 February 2017
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