Bergman-Einstein metrics, a generalization of Kerner's theorem and Stein spaces with spherical boundaries
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.
scientific article; zbMATH DE number 7291143