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Bergman kernel and metric on non-smooth pseudoconvex domains

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Abstract

A stability theorem of the Bergman kernel and completeness of the Bergman metric have been proved on a type of non-smooth pseudoconvex domains defined in the following way:D = {z∈U|r(z)} <whereU is a neighbourhood of\(\bar D\) andr is a continuous plurisubharmonic function onU. A continuity principle of the Bergman Kernel for pseudoconvex domains with Lipschitz boundary is also given, which answers a problem of Boas.

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Authors and Affiliations

  1. Institute of Mathematics, Fudan University, 200433, Shanghai, China

    Chen Boyong

  2. Department of Mathematics, Fudan University, 200433, Shanghai, China

    Zhang Jinhao

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  1. Chen Boyong
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  2. Zhang Jinhao
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Chen, B., Zhang, J. Bergman kernel and metric on non-smooth pseudoconvex domains. Sci. China Ser. A-Math. 42, 704–711 (1999). https://doi.org/10.1007/BF02878989

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  • DOI: https://doi.org/10.1007/BF02878989

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