Chordal Loewner chains with quasiconformal extensions
Pavel Gumenyuk, Ikkei Hotta
TL;DR
This paper develops a chordal analogue of Becker's classical construction for quasiconformal extensions using Loewner chains, providing new criteria for extendibility and simplifying existing proofs in the theory of holomorphic functions.
Contribution
It introduces a chordal version of Becker's construction, expanding the tools for quasiconformal extension criteria in complex analysis.
Findings
New sufficient conditions for quasiconformal extendibility.
Simplified proof of a classical result by Becker and Pommerenke.
Extension of Loewner chain techniques to the chordal setting.
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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Taxonomy
TopicsAnalytic and geometric function theory · Geometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations