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, NJ 08903, USA)

Xiaoshan Li (School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, China)

Abstract

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

Full Text (PDF format)

X.H. was upported by NSF grant DMS-2000050.  X.L. was supported by NSFC grant No. 11871380.

Received 26 September 2020

Accepted 15 June 2021

Published 26 July 2024