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J. Korean Math. Soc. 2016; 53(4): 769-780

Printed July 1, 2016

https://doi.org/10.4134/JKMS.j140595

Copyright © The Korean Mathematical Society.

Some rigidity theorems for self-shrinkers of the mean curvature flow

Hezi Lin

Fujian Normal University

Abstract

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In this paper, we first prove some Liouville type theorems for elliptic inequalities on weighted manifolds which support a weighted Sobolev-type inequality. Secondly, applying the Liouville type theorems to self-shrinkers, we obtain some global rigidity theorems.

Keywords: self-shrinkers, global rigidity, weighted manifolds

MSC numbers: Primary 53C44, 53C21

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