Communications in Analysis and Geometry

Volume 31 (2023)

Number 7

Bergman–Einstein metric on a Stein space with a strongly pseudoconvex boundary

Pages: 1669 – 1692

DOI: https://dx.doi.org/10.4310/CAG.2023.v31.n7.a3

Authors

Xiaojun Huang (Department of Mathematics, Rutgers University, New Brunswick, New Jersey, U.S.A.)

Xiaoshan Li (School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, China)

Abstract

Let $\Omega$ be a Stein space with a compact smooth strongly pseudo-convex boundary. We prove that the boundary is spherical if its Bergman metric over $\operatorname{Reg}(\Omega)$ is Kähler–Einstein.

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The first-named author was supported by NSF grant DMS-2000050.

The second-named author was supported by NSFC grant No. 11871380.

Received 26 September 2020

Accepted 15 June 2021

Published 10 August 2024