Chordal Loewner chains with quasiconformal extensions

2015/11/25 by Pavel Gumenyuk, Ikkei Hotta, Gumenyuk, Pavel +1
Mathematics · #Analytic and geometric function theory #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.CV #msc:30C45 #msc:30C55 #msc:30C62 #msc:30C80

paper · pdf · doi:10.48550/arxiv.1511.08077

arxiv created 2015/11/25 · arxiv updated 2015/11/26

Abstract

In 1972, Becker [J. Reine Angew. Math. 255 (1972), 23-43] 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 for functions in the half-plane [J. Reine Angew. Math. 354 (1984), 74-94].

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