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Transactions of the American Mathematical Society

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Asymptotic behavior of positively curved steady Ricci solitons


Authors: Yuxing Deng and Xiaohua Zhu
Journal: Trans. Amer. Math. Soc. 370 (2018), 2855-2877
MSC (2010): Primary 53C25; Secondary 53C55, 58J05
DOI: https://doi.org/10.1090/tran/7235
Published electronically: December 27, 2017
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Abstract: In this paper, we analyze the asymptotic behavior of $ \kappa $-noncollapsed and positively curved steady Ricci solitons and prove that any $ n$-dimensional $ \kappa $-noncollapsed steady Kähler-Ricci soliton with nonnegative sectional curvature must be flat.


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Additional Information

Yuxing Deng
Affiliation: School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China
Email: dengyuxing@mail.bnu.edu.cn

Xiaohua Zhu
Affiliation: School of Mathematical Sciences and BICMR, Peking University, Beijing, 100871, People’s Republic of China
Email: xhzhu@math.pku.edu.cn

DOI: https://doi.org/10.1090/tran/7235
Keywords: Ricci flow, Ricci soliton, $\kappa$-solution
Received by editor(s): February 8, 2016
Received by editor(s) in revised form: January 14, 2017
Published electronically: December 27, 2017
Additional Notes: The second author was partially supported by the NSFC Grants 11271022 and 11331001
Article copyright: © Copyright 2017 American Mathematical Society

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