Subdomain geometry of hyperbolic type metrics
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2012
- arXiv:
- arXiv:1212.0115
- Bibcode:
- 2012arXiv1212.0115K
- Keywords:
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- Mathematics - Metric Geometry;
- Primary 30F45;
- Secondary 30C65
- E-Print:
- 13 pages, 3 figures