Geometry of Reinhardt domains of finite type in \(\mathbb{C}^2\)
type: Item
instance of: scholarly article
title: Geometry of Reinhardt domains of finite type in \(\mathbb{C}^2\)
zbMATH Open document ID: 0920.32021
DOI: 10.1007/BF02921658
author: Siqi Fu
published in: The Journal of Geometric Analysis
publication date: 1999-08-31T00:00:00Z
review text: The author studies the asymptotic behavior of the holomorphic sectional curvature of the Bergman metric near boundary points of finite type of pseudoconvex Reinhardt domains in \(\mathbb{C}^2\) by comparing a domain locally to either a Thullen egg domain or a tube domain. On the model domains, explicit computations are feasible. The author deduces that the Bergman curvature is bounded between two negative constants in a neighborhood of a finite-type boundary point of a smoothly bounded pseudoconvex Reinhardt domain in \(\mathbb{C}^2\). It follows that every smooth, bounded, pseudoconvex, Reinhardt domain of finite type in \(\mathbb{C}^2\) admits a complete Kähler metric with holomorphic sectional curvature bounded between two negative constants.
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32A07
zbMATH DE Number: 1160127
zbMATH Keywords: Bergman metric
zbMATH Keywords: finite type
zbMATH Keywords: Reinhardt domain
zbMATH Keywords: tube domain
reviewed by: Harold P. Boas
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1160127