Sections of univalent harmonic mappings

In this article, we determine the radius of univalence of sections of normalized univalent harmonic mappings for which the range is convex (resp. starlike, close-to-convex, convex in one direction). Our result on the radius of univalence of section sn,n(f) is sharp especially when the corresponding mappings have convex range. In this case, each section sn,n(f) is univalent in the disk of radius 1/4 for all n≥2, which may be compared with classical result of Szegö on conformal mappings.