Some remarks on the Cassinian metric

Abstract

Some sharp inequalities between the triangular ratio metric and the Cassinian metric are proved in the unit ball.

15 pages, 2 figures

References in corpus (3)

• 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

Cited by in corpus (7)

• Barrlund's distance function and quasiconformal maps
• Intrinsic quasi-metrics
• Triangular ratio metric in the unit disk
• Metrics and quasimetrics induced by point pair function
• Remarks on the scale invariant Cassinian metric
• Intrinsic metrics in ring domains
• The Ptolemy-Alhazen problem and spherical mirror reflection