# Title:Mapping properties of a scale invariant Cassinian metric and a Gromov hyperbolic metric

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 Möbius 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.
 Comments: 13 pages (to appear in Bull. Aust. Math. Soc.) Subjects: Metric Geometry (math.MG) MSC classes: 51M10, 26A15, 30C20, 30C65, 30F45 Cite as: arXiv:1706.08643 [math.MG] (or arXiv:1706.08643v1 [math.MG] for this version)

## Submission history

[v1] Tue, 27 Jun 2017 01:55:28 UTC (11 KB)
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