Spherical density of hyperbolic metric and uniform perfectness

2015/03/05 by Toshiyuki Sugawa, Sugawa, Toshiyuki · 1 citation
Mathematics · #Analytic and geometric function theory #Holomorphic and Operator Theory #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1503.01519

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.

Cited by

• Spherical convexity and hyperbolic metric

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