Sharp entropy bounds for self-shrinkers in mean curvature flow

Or Hershkovits; Brian White

doi:10.2140/gt.2019.23.1611

Sharp entropy bounds for self-shrinkers in mean curvature flow

Or Hershkovits, Brian White

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Let M Ì Rm+1 be a smooth, closed, codimension-one self-shrinker (for mean curvature flow) with nontrivial k^th homology. We show that the entropy of M is greater than or equal to the entropy of a round k -sphere, and that if equality holds, then M is a round k-sphere in R^k+1.

Original language	American English
Pages (from-to)	1611-1619
Number of pages	9
Journal	Geometry and Topology
Volume	23
Issue number	3
DOIs	https://doi.org/10.2140/gt.2019.23.1611
State	Published - 2019
Externally published	Yes

Bibliographical note

Funding Information:
Hershkovits was partially supported by an AMS–Simons travel grant. partially supported by NSF grants DMS-1404282 and DMS-1711293.

Publisher Copyright:
© 2019, Mathematical Sciences Publishers. All rights reserved.

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10.2140/gt.2019.23.1611

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abstract = "Let M {\`I} Rm+1 be a smooth, closed, codimension-one self-shrinker (for mean curvature flow) with nontrivial kth homology. We show that the entropy of M is greater than or equal to the entropy of a round k -sphere, and that if equality holds, then M is a round k-sphere in Rk+1.",

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AB - Let M Ì Rm+1 be a smooth, closed, codimension-one self-shrinker (for mean curvature flow) with nontrivial kth homology. We show that the entropy of M is greater than or equal to the entropy of a round k -sphere, and that if equality holds, then M is a round k-sphere in Rk+1.

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Sharp entropy bounds for self-shrinkers in mean curvature flow

Abstract

Bibliographical note

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