Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (3): 839-850.doi: 10.1007/s10473-024-0304-y

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THE BOUNDARY SCHWARZ LEMMA AND THE RIGIDITY THEOREM ON REINHARDT DOMAINS Bpn OF Cnp OF Cn

Jianfei WANG1, Yanhui ZHANG2,*   

  1. 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).

Abstract: By introducing the Carathéodory metric, we establish the Schwarz lemma at the boundary for holomorphic self-mappings on the unit p-ball Bpn of Cn. Furthermore, the boundary rigidity theorem for holomorphic self-mappings defined on Bpn 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=, respectively.

Key words: Schwarz lemma, Carathéodory metric;, rigidity

CLC Number: 

  • 32H02
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