A Gromov Hyperbolic metric and M\"obius transformations
Complex Variables
2020-06-09 v1
Abstract
We compare a Gromov hyperbolic metric with the hyperbolic metric in the unit ball or in the upper half space, and prove sharp comparison inequalities between the Gromov hyperbolic metric and some hyperbolic type metrics. We also obtain several sharp distortion inequalities for the Gromov hyperbolic metric under some families of M\"{o}bius transformations.
Keywords
Cite
@article{arxiv.2006.04087,
title = {A Gromov Hyperbolic metric and M\"obius transformations},
author = {Xiaoxue Xu and Gendi Wang and Xiaohui Zhang},
journal= {arXiv preprint arXiv:2006.04087},
year = {2020}
}
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14 pages