English

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.

Keywords

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

R2 v1 2026-07-01T02:20:20.546Z