Chordal Loewner chains with quasiconformal extensions
Complex Variables
2015-11-26 v1
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].
Keywords
Cite
@article{arxiv.1511.08077,
title = {Chordal Loewner chains with quasiconformal extensions},
author = {Pavel Gumenyuk and Ikkei Hotta},
journal= {arXiv preprint arXiv:1511.08077},
year = {2015}
}