Year: 2026
Type: preprint
Abstract: We prove that a bounded pseudoconvex domain with piecewise $C^2$-smooth boundary which has a finite volume quotient for the complete Kähler-Einstein metric is biholomorphic to a product of complex unit balls. More generally, the same conclusion holds for a bounded domain possessing a boundary point satisfying Kodama's conditions (C.1)-(C.5), provided the quotient has finite volume for a complete $\operatorname{Aut}(D)$-invariant Kähler metric. For piecewise Levi-flat boundary the product is a polydisk and in the smooth pseudoconvex case it is a single ball.
Source: arXiv (Cornell University)
Authors: Pu, Xingsi, Wang, Lang
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221862419