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Schwarz lemma at the boundary and rigidity property for holomorphic mappings on the unit ball of $ \mathbb{C}^n$


Authors: Xiaomin Tang, Taishun Liu and Wenjun Zhang
Journal: Proc. Amer. Math. Soc. 145 (2017), 1709-1716
MSC (2010): Primary 32H02; Secondary 32A30, 30C80
DOI: https://doi.org/10.1090/proc/13378
Published electronically: October 20, 2016
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Abstract: In this paper, we first establish a new type of the classical Schwarz lemma at the boundary for holomorphic self-mappings of the unit ball in $ \mathbb{C}^n$, and then give the boundary version of the rigidity theorem.


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Additional Information

Xiaomin Tang
Affiliation: Department of Mathematics, Huzhou University, Huzhou 313000, Zhejiang, People’s Republic of China
Email: txm@zjhu.edu.cn

Taishun Liu
Affiliation: Department of Mathematics, Huzhou University, Huzhou 313000, Zhejiang, People’s Republic of China
Email: lts@ustc.edu.cn

Wenjun Zhang
Affiliation: College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, Guangdong, People’s Republic of China
Email: szuzwj@qq.com

DOI: https://doi.org/10.1090/proc/13378
Keywords: Holomorphic mapping, Schwarz lemma at the boundary, Rigidity
Received by editor(s): June 18, 2016
Published electronically: October 20, 2016
Additional Notes: This research was partially supported by NNSF of China (Nos. 11471111, 11571105) and NSF of Zhejiang Province(No. LY14A010017)
Communicated by: Lei Ni
Article copyright: © Copyright 2016 American Mathematical Society

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