Contraction property of certain classes of log-$\mathcal{M}-$subharmonic functions in the unit ball in $\mathbb{R}^n$

TL;DR

This paper establishes a contraction property for specific classes of smooth functions whose absolute values are log-hyperharmonic in the unit ball, extending prior results to higher dimensions and deriving new insights for harmonic mappings in the complex plane.

Contribution

It extends Kulikov's contraction results to higher-dimensional spaces and applies these findings to obtain new results for harmonic mappings in the complex plane.

Findings

Proved contraction property for log-$\\mathcal{M}$-subharmonic functions in higher dimensions

Extended Kulikov's results to the unit ball in $\mathbb{R}^n$

Derived new results for harmonic mappings in the complex plane

Abstract

We prove a contraction property of certain classes of smooth functions, whose absolute values of elements are log-hyperharmonic functions in the unit ball, thus extending the results of Kulikov to higher-dimensional space (GAFA (2022)). Moreover, by applying those results we get some new results for harmonic mappings in the complex plane.