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.

On a criterion of local invertibility and conformality for slice regular quaternionic functions / A. Gori, F. Vlacci. - In: PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY. - ISSN 0013-0915. - 62:1(2019 Feb), pp. 97-105. [10.1017/S0013091518000226]

On a criterion of local invertibility and conformality for slice regular quaternionic functions

A. Gori
Primo
;
2019-02

Abstract

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.
injective function of a hypercomplex variable; slice regular functions; Primary 30G35; 30C45
Settore MAT/03 - Geometria
Varietà reali e complesse: geometria, topologia e analisi armonica
28-ago-2018
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/611691
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