NDLI: Estimating the Error in the Koebe Construction

Content Provider	Springer Nature Link
Author	McNicholl, Timothy H. Andreev, Valentin V.
Copyright Year	2011
Abstract	In 1912, Paul Koebe proposed an iterative method, the Koebe construction, to construct a conformal mapping of a non-degenerate, finitely connected domain D onto a circular domain C [9]. In 1959, Gaier provided a convergence proof of the construction which depends on prior knowledge of the circular domain [5]. We demonstrate that it is possible to compute the convergence rate solely from information about D. We do so by computing a suitable bound on the error in the Koebe construction (but, again, without knowing the circular domain in advance) by using a relatively recent result on the distortion of capacity by Thurman [12] and a generalization of Schwarz-Pick Lemma by He and Schramm [7].
Starting Page	707
Ending Page	724
Page Count	18
File Format	PDF
ISSN	16179447
Journal	Computational Methods and Function Theory
Volume Number	11
Issue Number	2
e-ISSN	21953724
Language	English
Publisher	Springer-Verlag
Publisher Date	2013-04-02
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Numerical methods in conformal mapping theory Computational Mathematics and Numerical Analysis Functions of a Complex Variable Analysis Conformal mappings of special domains potential theory Capacity and harmonic measure in the complex plane multiply-connected domains capacity
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Theory and Mathematics Analysis

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