• Corpus ID: 119323000

# 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}
}```
• Published 1 December 2012
• Mathematics
• arXiv: Metric Geometry
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.
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