Mathematische Zeitschrift

, Volume 285, Issue 3–4, pp 1063–1089 | Cite as

Chordal Loewner chains with quasiconformal extensions

Article

Abstract

In 1972, Becker (J Reine Angew Math 255:23–43, 1972), discovered a construction of quasiconformal extensions making use of the classical radial Loewner chains. In this paper we develop a chordal analogue of Becker’s construction. As an application, we establish new sufficient conditions for quasiconformal extendibility of holomorphic functions and give a simplified proof of one well-known result by Becker and Pommerenke (J Reine Angew Math 354:74–94, 1984) for functions in the half-plane.

Keywords

Univalent function Quasiconformal extension Loewner chain Chordal Loewner equation Evolution family Loewner range 

Mathematics Subject Classification

Primary 30C62 Secondary 30C35 30D05 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institutt for matematikk og naturvitenskapUniversitetet i StavangerStavangerNorway
  2. 2.Department of Applied ScienceYamaguchi UniversityUbeJapan

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