4 problems

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…

Generalized Cheng conjecture. If the Bergman metric over $\operatorname{Reg}(\Omega)$ is Kähler–Einstein, then $\Omega$ is biholomorphic to $\mathbb B^n$.

Let $X$ be a finite dimensional reduced Stein space, and let $f\colon X\to \operatorname{Sp}_{2m}(\mathbb{C})$ be a holomorphic mapping that is null-homotopic. Let $M_1,\ldots,M_K$…

Modification characterization conjecture.