Quasihyperbolic metric and Möbius transformations

Details Quasihyperbolic metric and Möbius transformations Quasihyperbolic metric and Möbius transformations

2011-08-15

arxiv.org/abs/1108.2967v2

Mathematics

Complex Variables

12 pages

Scientific paper

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, 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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