Bergman-Einstein metrics, a generalization of Kerner's theorem and Stein spaces with spherical boundaries

Xiaojun Huang, Ming Xiao

Research output: Contribution to journalArticlepeer-review

Abstract

We give an affirmative solution to a conjecture of Cheng proposed in 1979 which asserts that the Bergman metric of a smoothly bounded strongly pseudoconvex domain in ℂ n, n ≥ 2, is Kähler-Einstein if and only if the domain is biholomorphic to the ball. We establish a version of the classical Kerner theorem for Stein spaces with isolated singularities which has an immediate application to construct a hyperbolic metric over a Stein space with a spherical boundary.

Original languageEnglish (US)
Pages (from-to)183-203
Number of pages21
JournalJournal fur die Reine und Angewandte Mathematik
Volume2021
Issue number770
DOIs
StatePublished - Jan 1 2021

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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