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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… Click to show full abstract
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. Finally, we establish the quasi-invariance properties of both metrics under quasiconformal maps.
Keywords:
cassinian metric;
scale invariant;
metric gromov;
invariant cassinian;
gromov hyperbolic;
hyperbolic metric
Journal Title: Bulletin of the Australian Mathematical Society
Year Published: 2017
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Journal Title: Bulletin of the Australian Mathematical Society
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!