Geometry of reinhardt domains of finite type in C2

Research output: Contribution to journalArticle

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)
JournalJournal of Geometric Analysis
Volume6
Issue number3
StatePublished - Dec 1 1996

Fingerprint

Reinhardt Domain
Finite Type
Bergman Metric
Sectional Curvature
Tube
Pseudoconvex Domain
Laplace Transformation
Fourier Transformation
Domain Model
Rescaling
Asymptotic Behavior
Metric

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

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

Cite this

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title = "Geometry of reinhardt domains of finite type in C2",
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.",
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author = "Siqi Fu",
year = "1996",
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language = "English (US)",
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journal = "Journal of Geometric Analysis",
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Geometry of reinhardt domains of finite type in C2. / Fu, Siqi.

In: Journal of Geometric Analysis, Vol. 6, No. 3, 01.12.1996.

Research output: Contribution to journalArticle

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AU - Fu, Siqi

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AB - 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.

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