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Geometry of Reinhardt domains of finite type in ℂ2

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Abstract

The asymptotic behavior of the holomorphic sectional curvature of the Bergman metric on a pseudoconvex Reinhardt domain of finite type in ℂ2 is obtained by rescaling locally the domain to a model domain that is either a Thullen domain Ω m = {(z 1,z 2); ¦z 1¦2 + ¦z 2¦2m < 1 or a tube domainT m = {(z 1,z 2); Imz1 + (Imz2)2m < 1}. The Bergman metric for the tube domainT m is explicitly calculated by using Fourier-Laplace transformation. It turns out that the holomorphic sectional curvature of the Bergman metric on the tube domainT m at (0, 0) is bounded above by a negative constant. These results are used to construct a complete Kähler metric with holomorphic sectional curvature bounded above by a negative constant for a pseudoconvex Reinhardt domain of finite type in ℂ2.

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  1. Siqi Fu

    Present address: Department of Mathematics, Texas A&M University, 77843, College Station, TX

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  1. Department of Mathematics, University of California, 92521, Riverside, CA

    Siqi Fu

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Fu, S. Geometry of Reinhardt domains of finite type in ℂ2 . J Geom Anal 6, 407–431 (1996). https://doi.org/10.1007/BF02921658

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