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Transactions of the American Mathematical Society

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A rigidity theorem on the second fundamental form for self-shrinkers


Author: Qi Ding
Journal: Trans. Amer. Math. Soc. 370 (2018), 8311-8329
MSC (2010): Primary 53A10, 53C24, 53C44
DOI: https://doi.org/10.1090/tran/7578
Published electronically: September 13, 2018
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Abstract: In Theorem 3.1 of The rigidity theorems of self-shrinkers (2014), the author and Y. L. Xin proved a rigidity result for self-shrinkers under the integral condition on the norm of the second fundamental form. In this paper, we relax such a bound to any finite constant (see Theorem 4.4 for details).


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Additional Information

Qi Ding
Affiliation: Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200438, China
Email: dingqi@fudan.edu.cn, dingqi09@fudan.edu.cn

DOI: https://doi.org/10.1090/tran/7578
Received by editor(s): January 23, 2017
Published electronically: September 13, 2018
Additional Notes: The author was supported partially by NSFC
Article copyright: © Copyright 2018 American Mathematical Society

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