Harmonic mappings, univalence criteria and a theorem of Lehtinen

The harmonic inner radius of a planar domain is the largest constant with which a univalence criterion via the Schwarzian derivative holds for harmonic mappings. We show that for the unit disk and for every domain 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.