Lindeloef theorem for harmonic mappings

摘要

We extend the classical Lindeloef theorem for harmonic mappings. Assume that f is an univalent harmonic mapping of the unit disk U onto a Jordan domain with C~1 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.