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 Ωm = {(z1, Z2); [Z1]2 + [Z2]2m < 1} or a tube domain Tm = {(z1, Z2); Imz1 + (Imz2)2m < 1}. The Bergman metric for the tube domain Tm is explicitly calculated by using Fourier-Laplace transformation. It turns out that the holomorphic sectional curvature of the Bergman metric on the tube domain Tm at (0, 0) is bounded above by a negative constant. These results are used to construct a complete Kahler metric with holomorphic sectional curvature bounded above by a negative constant for a pseudoconvex Reinhardt domain of finite type in C2.

Original languageEnglish (US)
Pages (from-to)407-431
Number of pages25
JournalJournal of Geometric Analysis
Volume6
Issue number3
DOIs
StatePublished - 1996
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • Bergman metric
  • Finite type
  • Pseudoconvex
  • Reinhardt domain
  • Tube domain

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