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.
Chordal Loewner chains with quasiconformal extensions
Gumenyuk P.;
2017-01-01
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.File in questo prodotto:
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