A1 Refereed original research article in a scientific journal
Intrinsic metrics under conformal and quasiregular mappings
Authors: Rainio Oona
Publisher: KOSSUTH LAJOS TUDOMANYEGYETEM
Publication year: 2022
Journal: Publicationes Mathematicae Debrecen
Journal name in source: PUBLICATIONES MATHEMATICAE-DEBRECEN
Journal acronym: PUBL MATH-DEBRECEN
Volume: 101
Issue: 1-2
First page : 189
Last page: 215
Number of pages: 27
ISSN: 0033-3883
DOI: https://doi.org/10.5486/PMD.2022.9263
Preprint address: https://arxiv.org/abs/2103.04397
Abstract
The distortion of six different intrinsic metrics and quasi-metrics under conformal and quasiregular mappings is studied in a few simple domains G C R-n. The already known inequalities between the hyperbolic metric and these intrinsic metrics for points x, y in the unit ball B-n are improved by limiting the absolute values of the points x, y, and the new results are then used to study the conformal distortion of the intrinsic metrics. For the triangular ratio metric between two points x, y is an element of B-n, the conformal distortion is bounded in terms of the hyperbolic midpoint and the hyperbolic distance of x, y. Furthermore, quasiregular and quasiconformal mappings are studied, and new sharp versions of the Schwarz lemma are introduced.
The distortion of six different intrinsic metrics and quasi-metrics under conformal and quasiregular mappings is studied in a few simple domains G C R-n. The already known inequalities between the hyperbolic metric and these intrinsic metrics for points x, y in the unit ball B-n are improved by limiting the absolute values of the points x, y, and the new results are then used to study the conformal distortion of the intrinsic metrics. For the triangular ratio metric between two points x, y is an element of B-n, the conformal distortion is bounded in terms of the hyperbolic midpoint and the hyperbolic distance of x, y. Furthermore, quasiregular and quasiconformal mappings are studied, and new sharp versions of the Schwarz lemma are introduced.
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