Sharp entropy bounds for self-shrinkers in mean curvature flow

IF 2 1区数学

Geometry & Topology Pub Date : 2018-03-01 DOI:10.2140/gt.2019.23.1611

Or Hershkovits, B. White

引用次数: 19

Abstract

Let $M\subset {\mathbf R}^{m+1}$ be a smooth, closed, codimension-one self-shrinker (for mean curvature flow) with nontrivial $k^{\rm th}$ 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 ${\mathbf R}^{k+1}$.

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平均曲率流中自收缩物的锐熵界

设$M\子集{\mathbf R}^{M +1}$是一个光滑的、封闭的、协维一的自收缩体(对于平均曲率流)，具有非平凡的$k^{\rm th}$同调。我们证明了$M$的熵大于或等于$k$-圆球的熵，如果等式成立，则$M$是${\mathbf R}^{k+1}$中的$k$-圆球。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Geometry & Topology 数学-数学

自引率

5.00%

发文量

期刊介绍： Geometry and Topology is a fully refereed journal covering all of geometry and topology, broadly understood. G&T is published in electronic and print formats by Mathematical Sciences Publishers. The purpose of Geometry & Topology is the advancement of mathematics. Editors evaluate submitted papers strictly on the basis of scientific merit, without regard to authors" nationality, country of residence, institutional affiliation, sex, ethnic origin, or political views.