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arXiv · 2604.00269

Harmonic mappings, univalence criteria and a theorem of Lehtinen

Iason Efraimidis·Rodrigo Hernández
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Abstract

The harmonic inner radius $\sigma_H(\Omega)$ of a planar domain $\Omega$ is the largest constant with which a univalence criterion via the Schwarzian derivative holds for harmonic mappings. We show that $\sigma_H(\Omega)\leq\sigma_H(\mathbb{D})\leq 3/2$ for the unit disk $\mathbb{D}$ and for every domain $\Omega$ that omits an open set. This is an analogue of a theorem of Lehtinen in the setting of holomorphic functions. We provide two related univalence criteria for harmonic mappings.

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Iason Efraimidis, Rodrigo Hernández. 2026-03-31. Harmonic mappings, univalence criteria and a theorem of Lehtinen. https://doi.org/10.1007/s41478-026-01157-y

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