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

References in corpus (8)

• Lipschitz conditions, triangular ratio metric, and quasiconformal maps
• Inequalities and bilipschitz conditions for triangular ratio metric
• Geometry of the Cassinian metric and its inner metric
• Some remarks on the Cassinian metric
• Barrlund's distance function and quasiconformal maps
• Triangular ratio metric under quasiconformal mappings in sector domains
• Triangular ratio metric in the unit disk
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Cited by in corpus (6)

• Triangular ratio metric under quasiconformal mappings in sector domains
• Intrinsic metrics under conformal and quasiregular mappings
• Metrics and quasimetrics induced by point pair function
• Möbius metric in sector domains
• Introducing a new intrinsic metric
• Intrinsic metrics in ring domains