On Koebe-type functions for harmonic quasiconformal mappings
Complex Variables
2026-01-05 v3
Abstract
This paper studies a class of Koebe-type harmonic quasiconformal functions. It is motivated by the shear construction of Clunie and Sheil-Small [Ann. Acad. Sci. Fenn. Ser. A I Math. 9: 3--25, 1984] and the harmonic quasiconformal Koebe function. Equivalent univalence conditions, pre-Schwarzian and Schwarzian norms, coefficient inequalities, as well as growth and area theorems for this family of functions are established. These findings improve several previously known results.
Cite
@article{arxiv.2505.12562,
title = {On Koebe-type functions for harmonic quasiconformal mappings},
author = {Zhi-Gang Wang and Jia-Le Qiu and Antti Rasila},
journal= {arXiv preprint arXiv:2505.12562},
year = {2026}
}
Comments
6 figures,to appear in Analysis Mathematica