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Boundary Regularity of Isometries Between Infinitely Flat Complex Domains

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Abstract

In this paper we prove that isometries with respect to the Kobayashi metric between certain domains having boundary points at which the boundary is infinitely flat extend continuously to the boundary. The strategy is to reestablish the Gehring-Hayman-type Theorem for these complex domains. Furthermore, the regularity of boundary extension map is given.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P. R. China

    Jin Song Liu

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, P. R. China

    Jin Song Liu

  3. Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, P. R. China

    Fei Tao

  4. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, P. R. China

    Hong Yu Wang

  5. Key Laboratory of Mathematics and Information Networks (Beijing University of Posts and Telecommunications), Ministry of Education, Beijing, 100876, P. R. China

    Hong Yu Wang

Authors
  1. Jin Song Liu
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  2. Fei Tao
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  3. Hong Yu Wang
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Corresponding author

Correspondence to Hong Yu Wang.

Ethics declarations

Conflict of Interest Jin Song LIU is an editorial board member for Acta Mathematica Sinica English Series and was not involved in the editorial review or the decision to publish this article. All authors declare that there are no competing interests.

Additional information

J. Liu is supported by National Key R&D Program of China (Grant No. 2021YFA1003100), NSFC (Grant Nos. 11925107 and 12226334), Key Research Program of Frontier Sciences, CAS (Grant No. ZDBS-LY-7002); H. Wang is supported by the Young Scientist Program of the Ministry of Science and Technology of China (Grant No. 2021YFA1002200) and NSFC (Grant No. 12201059)

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Liu, J.S., Tao, F. & Wang, H.Y. Boundary Regularity of Isometries Between Infinitely Flat Complex Domains. Acta. Math. Sin.-English Ser. (2024). https://doi.org/10.1007/s10114-024-1251-1

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  • DOI: https://doi.org/10.1007/s10114-024-1251-1

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