Abstract
In this paper, the author proves that the spacelike self-shrinker which is closed with respect to the Euclidean topology must be flat under a growth condition on the mean curvature by using the Omori-Yau maximum principle.
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Acknowledgement
The author would like to express his sincere gratitude to Professor Y. L. Xin for his valuable suggestions. He thanks Dr. Yong Luo for helpful discussion. He also thanks the Shanghai Center for Mathematical Sciences, where part of this work was done during his visit.
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This work was supported by the National Natural Science Foundation of China (No. 11771339), the Fundamental Research Funds for the Central Universities (No. 2042019kf0198) and the Youth Talent Training Program of Wuhan University.
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Qiu, H. A Rigidity Result of Spacelike Self-Shrinkers in Pseudo-Euclidean Spaces. Chin. Ann. Math. Ser. B 42, 291–296 (2021). https://doi.org/10.1007/s11401-021-0258-5
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DOI: https://doi.org/10.1007/s11401-021-0258-5