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

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

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

Cite this

Lakic, N., & Markowsky, G. T. (2012). The rate of convergence of the hyperbolic density on sequences of domains. In F. Bonahon, R. L. Devaney, F. P. Gardiner, & D. Saric (Eds.), Contemporary Mathematics - Conformal Dynamics and Hyperbolic Geometry (Vol. 573, pp. 147 - 157). Rhode Island USA: American Mathematical Society. https://doi.org/10.1090/conm/573/11377
Lakic, Nikola ; Markowsky, Gregory Tycho. / The rate of convergence of the hyperbolic density on sequences of domains. Contemporary Mathematics - Conformal Dynamics and Hyperbolic Geometry. editor / Francis Bonahon ; Robert L Devaney ; Frederick P Gardiner ; Dragomir Saric. Vol. 573 Rhode Island USA : American Mathematical Society, 2012. pp. 147 - 157
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Lakic, N & Markowsky, GT 2012, The rate of convergence of the hyperbolic density on sequences of domains. in F Bonahon, RL Devaney, FP Gardiner & D Saric (eds), Contemporary Mathematics - Conformal Dynamics and Hyperbolic Geometry. vol. 573, American Mathematical Society, Rhode Island USA, pp. 147 - 157, Conference on Conformal Dynamics and Hyperbolic Geometry 2010, New York, United States of America, 21/10/10. https://doi.org/10.1090/conm/573/11377

The rate of convergence of the hyperbolic density on sequences of domains. / Lakic, Nikola; Markowsky, Gregory Tycho.

Contemporary Mathematics - Conformal Dynamics and Hyperbolic Geometry. ed. / Francis Bonahon; Robert L Devaney; Frederick P Gardiner; Dragomir Saric. Vol. 573 Rhode Island USA : American Mathematical Society, 2012. p. 147 - 157.

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

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AU - Lakic, Nikola

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PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

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VL - 573

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BT - Contemporary Mathematics - Conformal Dynamics and Hyperbolic Geometry

A2 - Bonahon, Francis

A2 - Devaney, Robert L

A2 - Gardiner, Frederick P

A2 - Saric, Dragomir

PB - American Mathematical Society

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Lakic N, Markowsky GT. The rate of convergence of the hyperbolic density on sequences of domains. In Bonahon F, Devaney RL, Gardiner FP, Saric D, editors, Contemporary Mathematics - Conformal Dynamics and Hyperbolic Geometry. Vol. 573. Rhode Island USA: American Mathematical Society. 2012. p. 147 - 157 https://doi.org/10.1090/conm/573/11377