Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 401-418

QUASICONFORMAL HARMONIC MAPPINGS WITH THE CONVEX HOLOMORPHIC PART

Dariusz Partyka, Ken-ichi Sakan and Jian-Feng Zhu

The John Paul II Catholic University of Lublin, Institute of Mathematics and Computer Science
Al. Raclawickie 14, P.O. Box 129, 20-950 Lublin, Poland; partyka 'at' kul.lublin.pl
and The State School of Higher Education in Chelm, Institute of Mathematics and Information Technology
Pocztowa 54, 22-100 Chelm, Poland

Osaka City University, Graduate School of Science, Department of Mathematics
Sugimoto Sumiyoshi-ku, Osaka, 558-8585, Japan; ksakan 'at' sci.osaka-cu.ac.jp

Huaqiao University, School of Mathematical Sciences
Quanzhou-362021, P.R. China; flandy 'at' hqu.edu.cn

Abstract. Let F = H + \overline G be a locally injective and sense-preserving harmonic mapping of the unit disk D in the complex plane C, where H and G are holomorphic in D and G(0) =0. In this paper, under the assumption that H maps conformally D onto a convex domain we obtain modified forms of some results shown for a mapping F such that F(D) is a convex domain in C in the references [11] and [12].

2010 Mathematics Subject Classification: Primary 30C62, 30C55.

Key words: Harmonic mappings, quasiconformal mappings, Lipschitz condition, bi-Lipschitz condition, co-Lipschitz condition, Jacobian.

Reference to this article: D. Partyka, K. Sakan and J.-F. Zhu: Quasiconformal harmonic mappings with the convex holomorphic part. Ann. Acad. Sci. Fenn. Math. 43 (2018), 401-418.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4326