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Quasihyperbolic metric and Möbius transformations


Authors: Riku Klén, Matti Vuorinen and Xiaohui Zhang
Journal: Proc. Amer. Math. Soc. 142 (2014), 311-322
MSC (2010): Primary 30C65, 51M10
DOI: https://doi.org/10.1090/S0002-9939-2013-11765-X
Published electronically: October 4, 2013
MathSciNet review: 3119205
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Abstract | References | Similar Articles | Additional Information

Abstract: An improved version of the quasiinvariance property of the quasi-
hyperbolic metric under Möbius transformations of the unit ball in $ {\mathbb{R}}^n, n \ge 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.


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Additional Information

Riku Klén
Affiliation: Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland
Email: ripekl@utu.fi

Matti Vuorinen
Affiliation: Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland
Email: vuorinen@utu.fi

Xiaohui Zhang
Affiliation: Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland
Email: xiazha@utu.fi

DOI: https://doi.org/10.1090/S0002-9939-2013-11765-X
Keywords: Quasihyperbolic metric, distance-ratio metric, spherical metric, M\"obius transformation, quasiinvariance
Received by editor(s): August 23, 2011
Received by editor(s) in revised form: November 16, 2011, and March 13, 2012
Published electronically: October 4, 2013
Communicated by: Tatiana Toro
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.