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The rigidity theorems of self-shrinkers


Authors: Qi Ding and Y. L. Xin
Journal: Trans. Amer. Math. Soc. 366 (2014), 5067-5085
MSC (2010): Primary 53C44
DOI: https://doi.org/10.1090/S0002-9947-2014-05901-1
Published electronically: July 1, 2014
MathSciNet review: 3240917
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Abstract: By using certain techniques developed in minimal submanifold theory, we study the rigidity problem for self-shrinkers in the present paper. We prove rigidity results for the squared norm of the second fundamental form of self-shrinkers, either under pointwise conditions or under integral conditions.


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Additional Information

Qi Ding
Affiliation: Institute of Mathematics, Fudan University, Shanghai 200433, People’s Republic of China
Email: 09110180013@fudan.edu.cn

Y. L. Xin
Affiliation: Institute of Mathematics, Fudan University, Shanghai 200433, People’s Republic of China
Email: ylxin@fudan.edu.cn

DOI: https://doi.org/10.1090/S0002-9947-2014-05901-1
Received by editor(s): September 19, 2011
Published electronically: July 1, 2014
Additional Notes: This research was partially supported by NSFC
Article copyright: © Copyright 2014 American Mathematical Society