2026/03/31 by Iason Efraimidis, Rodrigo Hernández
Mathematics · #Analytic and geometric function theory #Meromorphic and Entire Functions #Holomorphic and Operator Theory
paper · pdf · doi:10.1007/s41478-026-01157-y
Abstract 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(\mathbb D)≤ 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.