Extremal decomposition problems in the Euclidean space

TL;DR

This paper extends composition principles for reduced moduli to higher-dimensional Euclidean spaces, leading to new extremal decomposition theorems analogous to classical planar results.

Contribution

It generalizes extremal decomposition theorems from the plane to n-dimensional Euclidean spaces using composition principles for reduced moduli.

Findings

Extended composition principles for reduced moduli to n-dimensional spaces

Derived analogues of classical extremal decomposition theorems

Established new theoretical results in geometric function theory

Abstract

Composition principles for reduced moduli are extended to the case of domains in the $n$-dimensional Euclidean space, $n>2$. As a consequence analogues of extremal decomposition theorems of Kufarev, Dubinin and Kirillova in the planer case are obtained.