Hyperbolic-type metrics in space

Aimo Hinkkanen; Poranee Khayo

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arXiv · 2605.27213

Hyperbolic-type metrics in space

Aimo Hinkkanen·Poranee Khayo

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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.

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Aimo Hinkkanen, Poranee Khayo. 2026-05-26. Hyperbolic-type metrics in space. https://arxiv.org/abs/2605.27213

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