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.

arXiv comment21 pages, 7 figures

References in corpus (9)

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• Inequalities and bilipschitz conditions for triangular ratio metric
• Some remarks on the Cassinian metric
• Barrlund's distance function and quasiconformal maps
• Intrinsic quasi-metrics
• Triangular ratio metric in the unit disk
• Intrinsic metrics under conformal and quasiregular mappings
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• Möbius metric in sector domains