Intrinsic quasi-metrics

Abstract

The point pair function $p_G$ defined in a domain $G⊊{\mathbb{R}}^n$ is shown to be a quasi-metric and its other properties are studied. For a convex domain $G⊊{\mathbb{R}}^n$, a new intrinsic quasi-metric called the function $w_G$ is introduced. Several sharp results are established for these two quasi-metrics, and their connection to the triangular ratio metric is studied.

18 pages, 1 figure