The Schwarz-Pick lemma for slice regular functions
Complex Variables
2013-02-12 v1
Abstract
The celebrated Schwarz-Pick lemma for the complex unit disk is the basis for the study of hyperbolic geometry in one and in several complex variables. In the present paper, we turn our attention to the quaternionic unit ball B. We prove a version of the Schwarz-Pick lemma for self-maps of B that are slice regular, according to the definition of Gentili and Struppa. The lemma has interesting applications in the fixed-point case, and it generalizes to the case of vanishing higher order derivatives.
Cite
@article{arxiv.1209.2060,
title = {The Schwarz-Pick lemma for slice regular functions},
author = {Cinzia Bisi and Caterina Stoppato},
journal= {arXiv preprint arXiv:1209.2060},
year = {2013}
}
Comments
to appear in Indiana Univ. Math. J., 21 pages