Schottky's theorem in $\mathbb{C}^n$

TL;DR

This paper provides a concise proof of Schottky's theorem applicable to general domains in complex n-dimensional space, unifying the cases for n=1 and n>1.

Contribution

It introduces a short, unified proof of Schottky's theorem that applies to all dimensions in complex analysis.

Findings

Proof works for both n=1 and n>1 cases

Simplifies understanding of Schottky's theorem in multiple dimensions

Enhances the theoretical framework of complex analysis

Abstract

The aim of this note is to give a proof of the Schottky theorem in general domains in $\mathbb{C}^n$. The proof is short and works for the cases $n = 1$ and $n > 1$ at the same time.