Intrinsic metrics in ring domains

Abstract

Three hyperbolic type metrics including the triangular ratio metric, the $j^{\ast }$-metric and the Möbius metric are studied in an annular ring. The Euclidean midpoint rotation is introduced as a method to create upper and lower bounds for these metrics, and their sharp inequalities are found. A new Möbius-invariant lower bound is proved for the conformal capacity of a general ring domain by using a symmetric quantity defined with the Möbius metric.

21 pages, 7 figures

References in corpus (6)

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