Inequalities and bi-Lipschitz conditions for the triangular ratio metric

DOI10.1216/RMJ-2017-47-4-1121zbMath1376.30019arXiv1411.2747OpenAlexW2269030894MaRDI QIDQ2409591

Xiao-Hui Zhang, Parisa Hariri, Matti Vuorinen

Publication date: 12 October 2017

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.2747

zbMATH Keywords

quasiconformal mappingsvisual angle metricdistance ratio metricbi-Lipschitz condition

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65)

Related Items (17)

Intrinsic metrics in ring domains ⋮ Some remarks on the visual angle metric ⋮ Comparison and Möbius quasi-invariance properties of Ibragimov's metric ⋮ Triangular ratio metric in the unit disk ⋮ Inequalities for the generalized point pair function ⋮ The Ptolemy–Alhazen problem and quadric surface mirror reflection ⋮ The Ptolemy-Alhazen problem and spherical mirror reflection ⋮ Triangular ratio metric under quasiconformal mappings in sector domains ⋮ Inclusion properties of the triangular ratio metric balls ⋮ Geometric properties of the triangular ratio metric and related metrics ⋮ Free distance ratio mappings in Banach spaces ⋮ Barrlund's distance function and quasiconformal maps ⋮ Intrinsic quasi-metrics ⋮ Isometries for the modulus metric are quasiconformal mappings ⋮ Metrics and quasimetrics induced by point pair function ⋮ Introducing a new intrinsic metric ⋮ Möbius metric in sector domains

This page was built for publication: Inequalities and bi-Lipschitz conditions for the triangular ratio metric