The rate of convergence of the hyperbolic density on sequences of domains

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Abstract

It is known that if a sequence of domains U-n converges to a domain U in the Caratheodory sense then the hyperbolic densities on U-n converge to the hyperbolic density on U. In this paper, we study the rate of convergence of the hyperbolic density under a slightly different mode of convergence. In doing so, we are led to consider two other densities on domains, the Teichmuller density and the three-point density. We obtain several results which give rates of convergence in various scenarios.
Original languageEnglish
Title of host publicationContemporary Mathematics - Conformal Dynamics and Hyperbolic Geometry
EditorsFrancis Bonahon, Robert L Devaney, Frederick P Gardiner, Dragomir Saric
Place of PublicationRhode Island USA
PublisherAmerican Mathematical Society
Pages147 - 157
Number of pages11
Volume573
ISBN (Print)9780821853481
DOIs
Publication statusPublished - 2012
EventConference on Conformal Dynamics and Hyperbolic Geometry 2010 - Graduate School and University Center of CUNY, New York, United States of America
Duration: 21 Oct 201023 Oct 2010

Conference

ConferenceConference on Conformal Dynamics and Hyperbolic Geometry 2010
CountryUnited States of America
CityNew York
Period21/10/1023/10/10

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