Harmonic mappings, univalence criteria and a theorem of Lehtinen
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911558715572224 |
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| author | Efraimidis, Iason Hernández, Rodrigo |
| author_facet | Efraimidis, Iason Hernández, Rodrigo |
| 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_00269 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Harmonic mappings, univalence criteria and a theorem of Lehtinen Efraimidis, Iason Hernández, Rodrigo Complex Variables 30C99, 30G30 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. |
| title | Harmonic mappings, univalence criteria and a theorem of Lehtinen |
| topic | Complex Variables 30C99, 30G30 |
| url | https://arxiv.org/abs/2604.00269 |