Möbius metric in sector domains

Abstract

The Möbius metric ${\delta }_G$ is studied in the cases where its domain $G$ is an open sector of the complex plane. We introduce upper and lower bounds for this metric in terms of the hyperbolic metric and the angle of the sector, and then use these results to find bounds for the distortion of the Möbius metric under quasiregular mappings defined in sector domains. Furthermore, we numerically study the Möbius metric and its connection to the hyperbolic metric in polygon domains.

arXiv comment27 pages, 5 figures

References in corpus (7)

• Lipschitz conditions, triangular ratio metric, and quasiconformal maps
• Inequalities and bilipschitz conditions for triangular ratio metric
• Triangular ratio metric under quasiconformal mappings in sector domains
• Intrinsic quasi-metrics
• Condenser capacity and hyperbolic perimeter
• Ptolemy constant and uniformity
• Condenser capacity and hyperbolic diameter

Cited by in corpus (1)

• Intrinsic metrics in ring domains