A metric that better approximates the hyperbolic metric

descriptionPublicationkeyboard_double_arrow_right Article 01 Feb 2022 English Publisher:American Mathematical Society (AMS)Journal:Conformal Geometry and Dynamics of the American Mathematical Society, volume 26, pages 1-9 (eissn: 1088-4173,

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Authors: Ma, William;

doi: 10.1090/ecgd/368

A metric that better approximates the hyperbolic metric

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Abstract

We introduce a metric, called the star metric, that gives us better upper bound of the hyperbolic metric than the Möbius invariant metric. We present various examples, and comparisons among the hyperbolic metric, the Möbius invariant metric and the star metric.

Keywords

Möbius invariant metric, Conformal mappings of special domains, General theory of univalent and multivalent functions of one complex variable, Conformal metrics (hyperbolic, Poincaré, distance functions), star metric, hyperbolic metric

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