Quasiconformal extensions, Loewner chains, and the lambda-Lemma

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Gumenyuk , P & Prause , I 2018 , ' Quasiconformal extensions, Loewner chains, and the lambda-Lemma ' , Analysis and mathematical physics , vol. 8 , no. 4 , pp. 621-635 . https://doi.org/10.1007/s13324-018-0247-3

Title: Quasiconformal extensions, Loewner chains, and the lambda-Lemma
Author: Gumenyuk, Pavel; Prause, Istvan
Contributor organization: Department of Mathematics and Statistics
Date: 2018-11
Language: eng
Number of pages: 15
Belongs to series: Analysis and mathematical physics
ISSN: 1664-2368
DOI: https://doi.org/10.1007/s13324-018-0247-3
URI: http://hdl.handle.net/10138/286197
Abstract: Becker (J Reine Angew Math 255: 23-43, 1972) discovered a sufficient condition for quasiconformal extendibility of Loewner chains. Many known conditions for quasiconformal extendibility of holomorphic functions in the unit disk can be deduced from his result. We give a new proof of (a generalization of) Becker's result based on Slodkowski's Extended.-Lemma. Moreover, we characterize all quasiconformal extensions produced by Becker's (classical) construction and use that to obtain examples in which Becker's extension is extremal (i. e. optimal in the sense of maximal dilatation) or, on the contrary, fails to be extremal.
Subject: Quasiconformal extension
Loewner chain
Becker extension
Evolution family
Loewner-Kufarev equation
Loewner range
111 Mathematics
Peer reviewed: Yes
Usage restriction: openAccess
Self-archived version: acceptedVersion

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