Published Paper
Inserted: 9 nov 2016
Last Updated: 11 mar 2019
Journal: Advances in Geometry
Volume: 18
Number: 1
Pages: 5--26
Year: 2018
Doi: https://doi.org/10.1515/advgeom-2017-0044
Abstract:
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