Lindelöf theorem for harmonic mappings

Abstract

We extend the classical Lindelöf theorem for harmonic mappings. Assume that f is an univalent harmonic mapping of the unit disk U onto a Jordan domain with C¹ boundary. Then the function arg(∂_ϕ(f(z))/z), where z = re^iϕ, has continuous extension to the boundary of the unit disk, under certain condition on f|_T.