Exhaustion of hyperbolic complex manifolds and relations to the squeezing function

TL;DR

This paper explores the exhaustion of hyperbolic complex manifolds by domain sequences and investigates the properties of boundary points, establishing connections with the squeezing function and pseudoconvexity.

Contribution

It characterizes hyperbolic complex manifolds exhausted by domain sequences and proves that spherically extreme boundary points are necessarily strongly pseudoconvex.

Findings

Hyperbolic complex manifolds can be characterized by exhausting sequences of domains.

Spherically extreme boundary points are shown to be strongly pseudoconvex.

The relationship between exhaustion sequences and boundary geometry is clarified.

Abstract

The purpose of this article is twofold. The first aim is to characterize an $n$-dimensional hyperbolic complex manifold $M$ exhausted by a sequence $\{\Omega_j\}$ of domains in $\mathbb C^n$ via an exhausting sequence $\{f_j\colon \Omega_j\to M\}$ such that $f_j^{-1}(a)$ converges to a boundary point $\xi_0 \in \partial \Omega$ for some point $a\in M$. Then, our second aim is to show that any spherically extreme boundary point must be strongly pseudoconvex.