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.

13 pages, 3 figures

References in corpus (1)

• Local Convexity Properties of Quasihyperbolic Balls in Punctured Space