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arXiv · 2505.12562

On Koebe-type functions for harmonic quasiconformal mappings

Zhi-Gang Wang·Jia-Le Qiu·Antti Rasila
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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.

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Zhi-Gang Wang, Jia-Le Qiu, Antti Rasila. 2025-05-18. On Koebe-type functions for harmonic quasiconformal mappings. https://arxiv.org/abs/2505.12562

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