A Note on the Bergman metric of Bounded homogeneous Domains

DOI10.1017/S0027763000009399zbMath1127.32008MaRDI QIDQ5421086

Takeo Ohsawa, Chifune Kai

Publication date: 22 October 2007

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.nmj/1182525233

zbMATH Keywords

potentialBergman metricSiegel domainshomogeneous domains

Mathematics Subject Classification ID

Invariant metrics and pseudodistances in several complex variables (32F45)

Related Items (12)

A method of potential scaling in the study of pseudoconvex domains with noncompact automorphism group ⋮ The d-boundedness of the Bergman metric on a kind of Hartogs domain ⋮ A vanishing theorem on generalized Cartan-Hartogs domain of the second type ⋮ Miscellanea on PSH functions and \(L^2\) methods on pseudoconvex domains ⋮ A characterization of the unit ball by a Kähler-Einstein potential ⋮ On the Kähler hyperbolicity with respect to the Bergman metric on a class of Hartogs domains ⋮ Unnamed Item ⋮ Variants of Hörmander's theorem on \(q\)-convex manifolds by a technique of infinitely many weights ⋮ A survey on the \(L^2\) extension theorems ⋮ Compactness of the \(\overline{\partial} \)-Neumann problem on domains with bounded intrinsic geometry ⋮ \(L^2\)-cohomology vanishing theorem on a type of generalized Cartan-Hartogs domain ⋮ A certain K\"ahler potential of the Poincar\'e metric and its characterization

Cites Work

• Unnamed Item
• Unnamed Item
• \(L^ 2\)-cohomology and index theorem for the Bergman metric
• Infinite dimensionality of the middle \(L^2\)-cohomology on non-compact Kähler hyperbolic manifolds
• Some studies on Siegel domains
• The Bergman metric on hyperconvex domains
• \(L_ 2\) cohomology of the Bergman metric for weakly pseudoconvex domains
• Representations of the affine transformation groups acting simply transitively on Siegel domains
• Kähler hyperbolicity and \(L_ 2\)-Hodge theory
• Hyperconvexity and Bergman completeness
• Jensen measures, hyperconvexity and boundary behaviour of the pluricomplex Green function
• Bergman completeness of hyperconvex manifolds

This page was built for publication: A Note on the Bergman metric of Bounded homogeneous Domains