Subharmonicity of the modulus of quasiregular harmonic mappings

TL;DR

This paper characterizes the values of q for which the q-th power of the modulus of K-quasiregular harmonic mappings is subharmonic, extending understanding of their harmonic and quasiregular properties.

Contribution

It precisely identifies all real q-values making |u|^q subharmonic for K-quasiregular harmonic mappings, a novel result in quasiregular harmonic analysis.

Findings

Identifies all q such that |u|^q is subharmonic

Provides conditions for subharmonicity in quasiregular harmonic mappings

Extends subharmonicity theory to quasiregular harmonic context

Abstract

In this note we determine all numbers $q\in \mathbf R$ such that $|u|^q$ is a subharmonic function, provided that $u$ is a $K-$quasiregular harmonic mappings in an open subset $\Omega$ of the Euclidean space $\mathbf R^n$.