Quotients of hyperbolic metrics
type: Item
instance of: scholarly article
title: Quotients of hyperbolic metrics
zbMATH Open document ID: 1467.30029
author: D. Minda
published in: Computational Methods and Function Theory
publication date: 2018-01-17T00:00:00Z
review text: The author estimates the quotient of the hyperbolic metrics of two hyperbolic domains on the Riemann sphere, one being a proper subset of the other. The bounds for the quotients are useful in complex dynamics. The purpose of this paper is to show their importance for the theory of hyperbolic metric. The quotient is shown to be close to \(1\) either on compact subsets of the proper sub-domain or near to the common boundary of the two domains. Necessary and sufficient conditions are given for the sharpness of the bounds. Altogether \(7\) examples illustrate the results.
reviewed by: Heinrich Begehr
Mathematics Subject Classification ID: 30F45
zbMATH DE Number: 6826981
zbMATH Keywords: hyperbolic metric
zbMATH Keywords: monotonicity property
zbMATH Keywords: boundary behavior
MaRDI profile type: Publication
full work available at URL: s40315-017-0195-1
OpenAlex ID: W2586493913
cites work: Normal families: a geometric perspective
cites work: The Poincaré Metric of Plane Domains
cites work: Hyperbolic distortion for holomorphic maps
cites work: Q3103241
cites work: Universal covering maps for variable regions
cites work: On analytic mappings of Riemann surfaces
cites work: Intrinsic Disks on a Riemann Surface
cites work: Absence of wandering domains for some real entire functions with bounded singular sets
cites work: Bloch constants
cites work: Q4458802
cites work: Q4314431
DOI: 10.1007/S40315-017-0195-1
description: scientific article; zbMATH DE number 6826981