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On a Criterion of Local Invertibility and Conformality for Slice Regular Quaternionic Functions

Part of: Generalized function theory Geometric function theory

Published online by Cambridge University Press:  28 August 2018

Anna Gori  and
Fabio Vlacci
Anna Gori
Affiliation:
Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano, Italy (anna.gori@unimi.it)
Fabio Vlacci
Affiliation:
Dipartimento di Matematica e Informatica ‘U. Dini’, Università di Firenze Viale Morgagni, 67/A, 50134 Firenze, Italy (vlacci@math.unifi.it)
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Abstract

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A new criterion for local invertibility of slice regular quaternionic functions is obtained. This paper is motivated by the need to find a geometrical interpretation for analytic conditions on the real Jacobian associated with a slice regular function f. The criterion involves spherical and Cullen derivatives of f and gives rise to several geometric implications, including an application to related conformality properties.

Keywords

injective function of a hypercomplex variableslice regular functions

MSC classification

Primary: 30G35: Functions of hypercomplex variables and generalized variables
Secondary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 1 , February 2019 , pp. 97 - 105
Copyright
Copyright © Edinburgh Mathematical Society 2018 

References

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5.Gori, A. and Vlacci, F., Starlikeness for functions of a hypercomplex variable, Proc. Amer. Math. Soc. 145(2) (2017), 791–804.Google Scholar