A1 Refereed original research article in a scientific journal
Quasihyperbolic metric and möbius transformations
Authors: Klén R., Vuorinen M., Zhang X.
Publisher: AMER MATHEMATICAL SOC
Publication year: 2014
Journal: Proceedings of the American Mathematical Society
Journal name in source: Proceedings of the American Mathematical Society
Journal acronym: P AM MATH SOC
Article number: PII S0002-9939(2013)11765-X
Volume: 142
Issue: 1
First page : 311
Last page: 322
Number of pages: 12
ISSN: 0002-9939
DOI: https://doi.org/10.1090/S0002-9939-2013-11765-X
Web address : http://api.elsevier.com/content/abstract/scopus_id:84886290221
Abstract
An improved version of the quasiinvariance property of the quasihyperbolic metric under Möbius transformations of the unit ball in R, n ≥ 2, is given, and a quasiinvariance property, sharp in a local sense, of the quasihyperbolic metric under quasiconformal mappings is proved. Finally, several inequalities between the quasihyperbolic metric and other commonly used metrics such as the hyperbolic metric of the unit ball and the chordal metric are established. © 2013 American Mathematical Society.
An improved version of the quasiinvariance property of the quasihyperbolic metric under Möbius transformations of the unit ball in R, n ≥ 2, is given, and a quasiinvariance property, sharp in a local sense, of the quasihyperbolic metric under quasiconformal mappings is proved. Finally, several inequalities between the quasihyperbolic metric and other commonly used metrics such as the hyperbolic metric of the unit ball and the chordal metric are established. © 2013 American Mathematical Society.
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