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arXiv · 1212.0115

Subdomain geometry of hyperbolic type metrics

Riku Klén·Yaxiang Li·Matti Vuorinen
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Abstract

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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Riku Klén, Yaxiang Li, Matti Vuorinen. 2012-12-01. Subdomain geometry of hyperbolic type metrics. https://arxiv.org/abs/1212.0115

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