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A Vanishing Theorem on a Class of Hartogs Domain

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Abstract

In this paper, we consider the d-boundedness of the Bergman metric and a vanishing theorem of L2-cohomology on a class of Hartogs domain, whose base domain is the production of two irreducible bounded symmetric domains of the first type, by using the Bergman kernel function, invariant function, holomorphic automorphism group and so on.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China

    Cheng Chen Zhong

  2. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, P. R. China

    An Wang

  3. Science College, Shijiazhuang University, Hebei, Shijiazhuang, 050035, P. R. China

    Li Shuang Pan

Authors
  1. Cheng Chen Zhong
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  2. An Wang
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  3. Li Shuang Pan
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Corresponding author

Correspondence to Cheng Chen Zhong.

Additional information

Supported by National Natural Science Foundation of China (Grant No. 11871044) Natural Science Foundation of Hebei Province (Grant No. A201906037)

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Zhong, C.C., Wang, A. & Pan, L.S. A Vanishing Theorem on a Class of Hartogs Domain. Acta. Math. Sin.-English Ser. 39, 1–12 (2023). https://doi.org/10.1007/s10114-022-0176-9

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  • DOI: https://doi.org/10.1007/s10114-022-0176-9

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