# Uniformization and Steinness

## TL;DR

This paper proves that the unit ball in complex n-space uniquely covers both Stein and non-Stein strictly pseudoconvex domains, highlighting its special role in complex geometry.

## Contribution

It establishes the uniqueness of the unit ball as the universal cover for certain classes of complex domains, linking uniformization and Steinness.

## Key findings

- The unit ball is the only universal cover for both Stein and non-Stein strictly pseudoconvex domains.
- This result characterizes the special status of the unit ball in complex manifold theory.
- The paper connects uniformization properties with Steinness in complex analysis.

## Abstract

It is shown that the unit ball in ${\mathbb C}^n$ is the only complex manifold that can universally cover both Stein and non-Stein strictly pseudoconvex domains.