# Subdomain geometry of hyperbolic type metrics

@article{Klen2012SubdomainGO, title={Subdomain geometry of hyperbolic type metrics}, author={Riku Kl'en and Yaxiang Li and Matti Vuorinen}, journal={arXiv: Metric Geometry}, year={2012} }

Given a domain $G \subsetneq \Rn$ we study the quasihyperbolic and the distance ratio metrics of $G$ and their connection to the corresponding metrics of a subdomain $D \subset G$. In each case, distances in the subdomain are always larger than in the original domain. Our goal is to show that, in several cases, one can prove a stronger domain monotonicity statement. We also show that under special hypotheses we have inequalities in the opposite direction.

## 2 Citations

MAPPING PROPERTIES OF A SCALE INVARIANT CASSINIAN METRIC AND A GROMOV HYPERBOLIC METRIC

- MathematicsBulletin of the Australian Mathematical Society
- 2017

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…

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