Three Balls Theorem for Eigenfunctions of Dirac Operator in Clifford Analysis

TL;DR

This paper proves a three balls inequality for eigenfunctions of the Dirac operator in Clifford analysis and extends Hadamard's three circles theorem to monogenic functions in higher dimensions.

Contribution

It introduces a three balls theorem for Dirac eigenfunctions and generalizes classical complex analysis results to Clifford analysis.

Findings

Established three balls inequality for Dirac eigenfunctions

Generalized Hadamard's three circles theorem to higher dimensions

Provided new tools for analysis of monogenic functions

Abstract

In this paper we establish the three balls theorem for functions $u$ satisfying $Du=\lambda u$ in Clifford analysis, where $D$ is the Dirac operator. As an application, we generalize Hadamard's three circles theorem to monogenic function in $\mathbb R^{n+1}.$