The open mapping theorem for regular quaternionic functions

TL;DR

This paper extends the theory of regular quaternionic functions by proving the minimum modulus principle and open mapping theorem, revealing unique geometric properties of these functions.

Contribution

It introduces the open mapping theorem for regular quaternionic functions, a significant advancement in understanding their geometric behavior.

Findings

Proved the minimum modulus principle for regular quaternionic functions

Established the open mapping theorem in the quaternionic setting

Identified unique geometric properties of these functions

Abstract

The basic results of a new theory of regular functions of a quaternionic variable have been recently stated, following an idea of Cullen. In this paper we prove the minimum modulus principle and the open mapping theorem for regular functions. The proofs involve some peculiar geometric properties of such functions which are of independent interest.