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Theoretical analysis shows harmonic inner radius limitations for domains, suggesting implications for mappings.
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 )≤ σ H(D)≤ 3/2 for the unit disk 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.
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Efraimidis et al. (2026) studied this question.
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