Spherical density of hyperbolic metric and uniform perfectness

Toshiyuki Sugawa

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arXiv · 1503.01519

Spherical density of hyperbolic metric and uniform perfectness

Toshiyuki Sugawa

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Abstract

It is well known that a hyperbolic domain in the complex plane has uniformly perfect boundary precisely when the product of its hyperbolic density and the distance function to its boundary has a positive lower bound. We extend this characterization to a hyperbolic domain in the Riemann sphere in terms of the spherical metric.

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Toshiyuki Sugawa. 2015-03-05. Spherical density of hyperbolic metric and uniform perfectness. https://arxiv.org/abs/1503.01519

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