6 problems

Let $D$ be a strongly pseudoconvex domain with smooth boundary. Let the Cheng–Yau metric be the canonical complete Kähler–Einstein metric on $D$, and let the Bergman metric be the…

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…

Let $D\subset\mathbb{C}^n$ be a bounded pseudoconvex domain. Its Bergman metric is the invariant Kähler metric associated with the Bergman kernel, and a domain is bounded homogeneo…

Let $M$ be a Stein manifold of complex dimension at least two, and let $A^2(M)$ be its Bergman space. Assume that $A^2(M)$ is base-point free and separates holomorphic directions.…

Let $M$ be a Stein manifold. Let $A^2(M)$ be its Bergman space, assumed to be base-point free, meaning that its sections do not vanish simultaneously at any point, and to separate…

A Stein manifold is a complex manifold admitting a proper holomorphic embedding into some complex Euclidean space. Its Bergman metric is the metric induced by its Bergman kernel wh…