Introducing a new intrinsic metric

Abstract

A new intrinsic metric called $t$-metric is introduced. Several sharp inequalities between this metric and the most common hyperbolic type metrics are proven for various domains $G⊊{\mathbb{R}}^n$. The behaviour of the new metric is also studied under a few examples of conformal and quasiconformal mappings, and the differences between the balls drawn with all the metrics considered are compared by both graphical and analytical means.

arXiv comment20 pages, 8 figures

References in corpus (7)

• 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
• Intrinsic quasi-metrics
• Barrlund's distance function and quasiconformal maps
• Triangular ratio metric under quasiconformal mappings in sector domains
• Triangular ratio metric in the unit disk

Cited by in corpus (2)

• Intrinsic quasi-metrics
• Intrinsic metrics under conformal and quasiregular mappings