$p$-Skwarczy\'nski distance

TL;DR

This paper introduces a novel distance measure on complex domains based on minimizer functions in a specific function space, exploring its mathematical properties such as invariance and completeness.

Contribution

The paper presents a new distance on complex domains derived from minimizer functions in $A^p(\Omega)$, analyzing its key mathematical properties.

Findings

The new distance is invariant under certain transformations.

The distance is complete under specific conditions.

Properties of the distance relate to the structure of $A^p(\Omega)$.

Abstract

We introduce a new distance on a domain $\Omega \subset \mathbb{C}^n$ using the `minimizer' functions on $A^p(\Omega)$. We discuss its invariance, completeness, and other aspects related to it.