Bergman-Einstein metrics, a generalization of Kerner's theorem and Stein spaces with spherical boundaries
type: Item
instance of: scholarly article
title: Bergman-Einstein metrics, a generalization of Kerner's theorem and Stein spaces with spherical boundaries
zbMATH Open document ID: 1462.32039
author: Xiaojun Huang
author: Ming Xiao
published in: Journal für die Reine und Angewandte Mathematik
publication date: 2021-01-08T00:00:00Z
review text: This paper proves that the Bergman metric of a smoothly bounded strongly pseudoconvex domain in \(\mathbb{C}^n\), \(n \ge 2\), is Kähler-Einstein if and only if the domain is biholomorphic to the ball. This was conjectured by \textit{S.Y. Cheng} [Open problems, in: Conference on Nonlinear Problems in Geometry (Katata 1979), Tohoku University, Sendai (1979; Zbl 0433.53002)]. The authors also establish a version of the classical Kerner theorem for Stein spaces with isolated singularities, which concerns holomorphic continuations of certain continuous CR map elements and has an application to construct a hyperbolic metric over a Stein space with a spherical boundary.
reviewed by: Yoshinori Hashimoto
Mathematics Subject Classification ID: 32T15
Mathematics Subject Classification ID: 32Q20
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 7291143
zbMATH Keywords: Bergman metrics
zbMATH Keywords: Kähler-Einstein metrics
zbMATH Keywords: Kerner theorem
zbMATH Keywords: Stein spaces
MaRDI profile type: Publication
full work available at URL: crelle-2020-0012
OpenAlex ID: W3030939534
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DOI: 10.1515/CRELLE-2020-0012
description: scientific article; zbMATH DE number 7291143