Every connected bounded domain of holomorphy has connected boundary

TL;DR

This paper proves that in complex analysis, every connected, bounded domain of holomorphy in higher dimensions has a boundary that is also connected, resolving a topological property of such domains.

Contribution

It establishes that all connected, bounded domains of holomorphy in complex spaces of dimension two or higher have connected boundaries, a previously unresolved topological feature.

Findings

Connected bounded domains of holomorphy have connected boundaries.

The result applies to complex spaces of dimension two or higher.

It advances understanding of the topological structure of holomorphic domains.

Abstract

It is shown that every connected, bounded domain of holomorphy in ${\mathbb{C}}^n$, $n\geq 2$, has connected boundary.