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arXiv · 1108.2967

Quasihyperbolic metric and M\"obius transformations

Riku Klén·Matti Vuorinen·Xiaohui Zhang
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Abstract

An improved version of quasiinvariance property of the quasihyperbolic metric under M\"obius transformations of the unit ball in ${\mathbb R}^n, n \ge 2,$ is given. Next, 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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Riku Klén, Matti Vuorinen, Xiaohui Zhang. 2011-08-15. Quasihyperbolic metric and M\"obius transformations. https://arxiv.org/abs/1108.2967

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