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Intrinsic metrics under conformal and quasiregular mappings
Tekijät: Rainio Oona
Kustantaja: KOSSUTH LAJOS TUDOMANYEGYETEM
Julkaisuvuosi: 2022
Journal: Publicationes Mathematicae Debrecen
Tietokannassa oleva lehden nimi: PUBLICATIONES MATHEMATICAE-DEBRECEN
Lehden akronyymi: PUBL MATH-DEBRECEN
Vuosikerta: 101
Numero: 1-2
Aloitussivu: 189
Lopetussivu: 215
Sivujen määrä: 27
ISSN: 0033-3883
DOI: https://doi.org/10.5486/PMD.2022.9263
Preprintin osoite: https://arxiv.org/abs/2103.04397
Tiivistelmä
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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