The \(C^{\infty }\)-convergence of circle packings of bounded degree to the Riemann mapping
type: Item
instance of: scholarly article
title: The \(C^{\infty }\)-convergence of circle packings of bounded degree to the Riemann mapping
zbMATH Open document ID: 1218.30011
author: Shiyi Lan
author: Dao-Qing Dai
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-02-09T00:00:00Z
review text: \textit{B. Rodin} and \textit{D. Sullivan} [J. Differ. Geom. 26, 349--360 (1987; Zbl 0694.30006)] proved the conjecture that the Riemann mapping function from a simply connected region onto the unit disk can be approximated by regular hexagonal pattern due to \textit{W. P. Thurston} [``The finite Riemann mapping theorem'', in: International symposium in celebration of the proof of the Bieberbach conjecture, Purdue University (1985)]. Corresponding to a result due to \textit{Z.-X. He} and \textit{O. Schramm} [Acta Math. 180, No. 2, 219--245 (1998; Zbl 0913.30004)], the authors generalize the \(C^\infty \) convergence to the case of non-hexagonal packings with bounded degree.
reviewed by: H. P. Dikshit
Mathematics Subject Classification ID: 30C30
zbMATH DE Number: 5848855
zbMATH Keywords: circle packings
zbMATH Keywords: bounded degree
zbMATH Keywords: Riemann mapping
describes a project that uses: CirclePack
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.11.043
OpenAlex ID: W2020079750
cites work: Q4297501
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DOI: 10.1016/J.JMAA.2010.11.043
description: scientific article; zbMATH DE number 5848855