Yau's finite-volume quotient conjecture for bounded pseudoconvex domains

Let $D earrow\mathbb{C}^n$ $(n\geq 2)$ be a bounded pseudoconvex domain whose boundary is $C^2$-smooth. Assume that $D$ has an open quotient of finite volume in the sense of Kähler–Einstein measure. Yau's conjecture. The domain $D$ is biholomorphic to the unit ball in $\mathbb{C}^n$. This conjecture asks whether the compact-quotient hypothesis in the Wong–Rosay theorem can be replaced by finite volume. The source reports partial results and notes a later claim by A. Zimmer of a solution; the supplied status is unknown, so the database status remains open.