Hyperbolic-type metrics in space
Complex Variables
2026-05-27 v1
Abstract
We define metrics in space that are natural counterparts of the hyperbolic metric in plane domains, using the characterization of the hyperbolic metric due to Beardon and Pommerenke. We obtain inequalities for these metrics under quasiconformal homeomorphisms between domains in space that have at least two boundary points. We discuss the failure of the existence of such estimates for non-homeomorphic quasiregular mappings.
Cite
@article{arxiv.2605.27213,
title = {Hyperbolic-type metrics in space},
author = {Aimo Hinkkanen and Poranee Khayo},
journal= {arXiv preprint arXiv:2605.27213},
year = {2026}
}