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The boundary Schwarz lemma and the rigidity theorem on Reinhardt domains B np of ℂn

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Abstract

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

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Authors and Affiliations

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, China

    Jianfei Wang

  2. Department of Mathematics, Beijing Technology and Business University, Beijing, 100048, China

    Yanhui Zhang

Authors
  1. Jianfei Wang
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  2. Yanhui Zhang
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Correspondence to Yanhui Zhang.

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Conflict of Interest The authors declare no conflict of interest.

Additional information

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).

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Wang, J., Zhang, Y. The boundary Schwarz lemma and the rigidity theorem on Reinhardt domains B np of ℂn. Acta Math Sci 44, 839–850 (2024). https://doi.org/10.1007/s10473-024-0304-y

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  • DOI: https://doi.org/10.1007/s10473-024-0304-y

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