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 \(\sigma _H(\Omega )\le \sigma _H({\mathbb {D}})\le 3/2\) 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.
