Geometria Complessa e Geometria Differenziale
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A. Altavilla

On the real differential of a slice regular function

created by stoppato on 09 Nov 2016
modified by altavilla on 11 Mar 2019


Published Paper

Inserted: 9 nov 2016
Last Updated: 11 mar 2019

Journal: Advances in Geometry
Volume: 18
Number: 1
Pages: 5--26
Year: 2018

ArXiv: 1402.3993 PDF
Links: journal page, arXiv


In this paper we show that the real differential of any injective slice regular function is everywhere invertible. The result is a generalization of a theorem proved by G. Gentili, S. Salamon and C. Stoppato, and it is obtained thanks, in particular, to some new information regarding the first coefficients of a certain polynomial expansion for slice regular functions (called \textit{spherical expansion}), and to a new general result which says that the slice derivative of any injective slice regular function is different from zero. A useful tool proven in this paper is a new formula that relates slice and spherical derivatives of a slice regular function. Given a slice regular function, part of its singular set is described as the union of surfaces on which it results to be constant.

Tags: FIRB2012-DGGFT

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