Every biregular function is a biholomorphic map
type: Item
instance of: scholarly article
title: Every biregular function is a biholomorphic map
zbMATH Open document ID: 1173.30035
author: Alessandro Perotti
published in: Advances in Applied Clifford Algebras
publication date: 2009-08-11T00:00:00Z
review text: The set of (left) Fueter-biregular functions of one quaternionic variable is considered. The aim of the paper is to give a characterization of biregular functions by means of holomorphy with respect to the orthogonal almost complex structures defined on dense, open subsets of a set \(\Omega\) in \({\mathbb H}\). A criterion, based on the energy-minimizing property of holomorphic maps, that distinguishes (pseudo) holomorphic functions among regular functions is proved. A formula is presented which expresses the determinant of the energy quadric as a polynomial in the first derivatives of the function. This formula is used to show that, for every biregular function, there exist a dense, open subset \(\Omega^{\prime}\) of \(\Omega\) and an almost complex \(p(z)\) on \(\Omega^{\prime}\) such that the function belongs to the set \(\text{Hol}_p(\Omega^{\prime}, {\mathbb H})\).
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 32A30
zbMATH DE Number: 5593792
zbMATH Keywords: quaternionic regular function
zbMATH Keywords: biregular function
zbMATH Keywords: holomorphic map
zbMATH Keywords: energy minimizing property
reviewed by: Sergei V. Rogosin
MaRDI profile type: Publication
full work available at URL: s00006-009-0161-8
OpenAlex ID: W2021907396
DOI: 10.1007/S00006-009-0161-8
description: scientific article; zbMATH DE number 5593792