Mapping properties of a scale invariant Cassinian metric and a Gromov hyperbolic metric
Metric Geometry
2017-06-28 v1
Abstract
In this paper, we consider a scale invariant Cassinian metric and a Gromov hyperbolic metric. We discuss a distortion property of the scale invariant Cassinian metric under M\"obius maps of a punctured ball onto another punctured ball. We obtain a modulus of continuity of the identity map from a domain equipped with the scale invariant Cassinian metric (or the Gromov hyperbolic metric) onto the same domain equipped with the Euclidean metric. The quasi-invariance properties of both the metrics under quasiconformal maps are also established.
Keywords
Cite
@article{arxiv.1706.08643,
title = {Mapping properties of a scale invariant Cassinian metric and a Gromov hyperbolic metric},
author = {Manas Ranjan Mohapatra and Swadesh Kumar Sahoo},
journal= {arXiv preprint arXiv:1706.08643},
year = {2017}
}
Comments
13 pages (to appear in Bull. Aust. Math. Soc.)