English

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 KK-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 KK-quasiconformal harmonic mappings of the unit disk onto a radial John disk. Finally, using Pommerenke interior domains, we characterize certain differential properties of KK-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