## Journal of the Mathematical Society of Japan

### Classification and rigidity of self-shrinkers in the mean curvature flow

#### Abstract

In this paper, we first use the method of Colding and Minicozzi II [7] to show that K. Smoczyk's classification theorem [25] for complete self-shrinkers in higher codimension also holds under a weaker condition. Then as an application, we give some rigidity results for self-shrinkers in arbitrary codimension.

#### Article information

Source
J. Math. Soc. Japan, Volume 66, Number 3 (2014), 709-734.

Dates
First available in Project Euclid: 24 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1406206969

Digital Object Identifier
doi:10.2969/jmsj/06630709

Mathematical Reviews number (MathSciNet)
MR3238314

Zentralblatt MATH identifier
1320.53074

#### Citation

LI, Haizhong; WEI, Yong. Classification and rigidity of self-shrinkers in the mean curvature flow. J. Math. Soc. Japan 66 (2014), no. 3, 709--734. doi:10.2969/jmsj/06630709. https://projecteuclid.org/euclid.jmsj/1406206969

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