• 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}
}
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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