Radial length, radial John disks and $K$-quasiconformal harmonic mappings
Complex Variables
2017-01-27 v1
Abstract
In this article, we continue our investigations of the boundary behavior of harmonic mappings. We first discuss the classical problem on the growth of radial length and obtain a sharp growth theorem of the radial length of -quasiconformal harmonic mappings. Then we present an alternate characterization of radial John disks. In addition, we investigate the linear measure distortion and the Lipschitz continuity on -quasiconformal harmonic mappings of the unit disk onto a radial John disk. Finally, using Pommerenke interior domains, we characterize certain differential properties of -quasiconformal harmonic mappings.
Keywords
Cite
@article{arxiv.1701.07537,
title = {Radial length, radial John disks and $K$-quasiconformal harmonic mappings},
author = {Shaolin Chen and Saminathan Ponnusamy},
journal= {arXiv preprint arXiv:1701.07537},
year = {2017}
}
Comments
23 pages; The article with a journal for publication