Quasihyperbolic metric and Möbius transformations

Klén, Riku; Vuorinen, Matti; Zhang, Xiaohui

doi:10.1090/S0002-9939-2013-11765-X

Quasihyperbolic metric and Möbius transformations
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by Riku Klén, Matti Vuorinen and Xiaohui Zhang PDF

Proc. Amer. Math. Soc. 142 (2014), 311-322 Request permission

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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