A characterization of bounded balanced convex domains in $\mathbb{C}^n$

TL;DR

This paper studies the properties of balanced bounded convex domains in complex n-space using the squeezing function, and characterizes the polydisc as a special case.

Contribution

It provides a new characterization of balanced bounded convex domains and identifies the polydisc within this class using the squeezing function.

Findings

Characterization of balanced bounded convex domains via the squeezing function

Identification of the polydisc as a specific case within these domains

Advancement in understanding geometric properties of complex domains

Abstract

In this paper, we investigate the characterization of balanced bounded convex domains in $\mathbb{C}^n$ in terms of the squeezing function. As an application, we provide a characterization of the polydisc in $\mathbb{C}^n$.