THE BOUNDARY SCHWARZ LEMMA AND THE RIGIDITY THEOREM ON REINHARDT DOMAINS $B_{p}^{n}$ OF $\mathbb{C}^{n}$p OF Cn

THE BOUNDARY SCHWARZ LEMMA AND THE RIGIDITY THEOREM ON REINHARDT DOMAINS $B_{p}^{n}$ OF $\mathbb{C}^{n}$ p OF Cn

THE BOUNDARY SCHWARZ LEMMA AND THE RIGIDITY THEOREM ON REINHARDT DOMAINS $B_{p}^{n}$ OF $\mathbb{C}^{n}$ p OF Cn

THE BOUNDARY SCHWARZ LEMMA AND THE RIGIDITY THEOREM ON REINHARDT DOMAINS $B_{p}^{n}$ OF $\mathbb{C}^{n}$ p OF Cn

THE BOUNDARY SCHWARZ LEMMA AND THE RIGIDITY THEOREM ON REINHARDT DOMAINS $B_{p}^{n}$ OF $\mathbb{C}^{n}$ p OF Cn

THE BOUNDARY SCHWARZ LEMMA AND THE RIGIDITY THEOREM ON REINHARDT DOMAINS BpnB_{p}^{n} OF Cn\mathbb{C}^{n}p OF Cn

THE BOUNDARY SCHWARZ LEMMA AND THE RIGIDITY THEOREM ON REINHARDT DOMAINS BpnB_{p}^{n} OF Cn\mathbb{C}^{n}p OF Cn

THE BOUNDARY SCHWARZ LEMMA AND THE RIGIDITY THEOREM ON REINHARDT DOMAINS $B_{p}^{n}$ OF $\mathbb{C}^{n}$ p OF Cn

THE BOUNDARY SCHWARZ LEMMA AND THE RIGIDITY THEOREM ON REINHARDT DOMAINS $B_{p}^{n}$ OF $\mathbb{C}^{n}$ p OF Cn

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doi:10.1007/s10473-024-0304-y

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (3): 839-850.doi: 10.1007/s10473-024-0304-y

Jianfei WANG¹, Yanhui ZHANG^2,*

1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;
2. Department of Mathematics, Beijing Technology and Business University, Beijing 100048, China

收稿日期:2022-10-10 修回日期:2023-02-21 出版日期:2024-06-25 发布日期:2024-05-21

Jianfei WANG¹, Yanhui ZHANG^2,*

1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;
2. Department of Mathematics, Beijing Technology and Business University, Beijing 100048, China

Received:2022-10-10 Revised:2023-02-21 Online:2024-06-25 Published:2024-05-21
Contact: *Yanhui ZHANG,E-mail:zhangyanhui@th.btbu.edu.cn
About author:Jianfei WANG,E-mail:wangjf@mail.ustc.edu.cn
Supported by:
Wang's research was supported by the National Natural Science Foundation of China (12071161, 11971165) and the Natural Science Foundation of Zhejiang Province (Z24A010005). Zhang's research was supported by the National Natural Science Foundation of China (11971042).

摘要： By introducing the Carathéodory metric, we establish the Schwarz lemma at the boundary for holomorphic self-mappings on the unit $p$ -ball $B_{p}^{n}$ of $\mathbb{C}^n$ . Furthermore, the boundary rigidity theorem for holomorphic self-mappings defined on $B_{p}^{n}$ is obtained. These results cover the boundary Schwarz lemma and rigidity result for holomorphic self-mappings on the unit ball for $p=2$ , and the unit polydisk for $p=\infty$ , respectively.

关键词: Schwarz lemma, Carathéodory metric;, rigidity

Abstract: By introducing the Carathéodory metric, we establish the Schwarz lemma at the boundary for holomorphic self-mappings on the unit $p$ -ball $B_{p}^{n}$ of $\mathbb{C}^n$ . Furthermore, the boundary rigidity theorem for holomorphic self-mappings defined on $B_{p}^{n}$ is obtained. These results cover the boundary Schwarz lemma and rigidity result for holomorphic self-mappings on the unit ball for $p=2$ , and the unit polydisk for $p=\infty$ , respectively.

Key words: Schwarz lemma, Carathéodory metric;, rigidity

中图分类号:

32H02

Jianfei WANG, Yanhui ZHANG. THE BOUNDARY SCHWARZ LEMMA AND THE RIGIDITY THEOREM ON REINHARDT DOMAINS $B_{p}^{n}$ OF $\mathbb{C}^{n}$ p OF Cn[J]. 数学物理学报(英文版), 2024, 44(3): 839-850.

Jianfei WANG, Yanhui ZHANG. THE BOUNDARY SCHWARZ LEMMA AND THE RIGIDITY THEOREM ON REINHARDT DOMAINS $B_{p}^{n}$ OF $\mathbb{C}^{n}$ p OF Cn[J]. Acta mathematica scientia,Series B, 2024, 44(3): 839-850.

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