Möbius metric in sector domains

Abstract

The Mobius 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 Mobius metric under quasiregular mappings defined in sector domains. Furthermore, we numerically study the Mobius metric and its connection to the hyperbolic metric in polygon domains.