Journal of the Mathematical Society of Japan

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

Haizhong LI and Yong WEI

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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

Subjects
Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)

Keywords
self-shrinker rigidity mean curvature flow

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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