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arXiv · 1402.3993

On the real differential of a slice regular function

Amedeo Altavilla
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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.

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Amedeo Altavilla. 2016-05-27. On the real differential of a slice regular function. https://doi.org/10.1515/advgeom-2017-0044

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