Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 66, Number 3 (2014), 709-734.
Classification and rigidity of self-shrinkers in the mean curvature flow
In this paper, we first use the method of Colding and Minicozzi II  to show that K. Smoczyk's classification theorem  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.
J. Math. Soc. Japan, Volume 66, Number 3 (2014), 709-734.
First available in Project Euclid: 24 July 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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.)
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