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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.00269 |
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Table of Contents:
- The harmonic inner radius $σ_H(Ω)$ of a planar domain $Ω$ is the largest constant with which a univalence criterion via the Schwarzian derivative holds for harmonic mappings. We show that $σ_H(Ω)\leqσ_H(\mathbb{D})\leq 3/2$ for the unit disk $\mathbb{D}$ and for every domain $Ω$ 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.