Problems on extremal decomposition of the complex plane

TL;DR

This paper investigates the problem of identifying extremal configurations that maximize the product of inner radii of non-overlapping domains in the complex plane, providing insights into geometric optimization.

Contribution

It introduces a general framework for describing extremal configurations related to the product of inner radii in non-overlapping domains in the complex plane.

Findings

Characterization of extremal configurations

Maximization of the product of inner radii

General conditions for extremality

Abstract

Considered here is one quite general problem about description of extremal configurations maximizing the product of inner radii non-overlapping domains.