Huang–Xiao's uniformization conjecture for Stein spaces

Let $\Omega$ be a normal Stein space with a compact, smooth, strongly pseudoconvex boundary. Let $\Omega_{\operatorname{Reg}}$ denote its regular part, and let the Bergman metric be the metric induced by the Bergman kernel on this regular part. Huang–Xiao's conjecture. The Bergman metric on $\Omega_{\operatorname{Reg}}$ is Kähler–Einstein if and only if $\Omega$ is biholomorphic to the unit ball in a complex Euclidean space. This is a uniformization statement extending Cheng's conjecture from smooth domains and Stein manifolds to normal Stein spaces with isolated singularities; the source presents it as a generalization later addressed by the paper.