Widomski, Jarosław; Gregorczyk, Magdalena Harmonic mappings in the exterior of the unit disk. (English) Zbl 1213.30042 Ann. Univ. Mariae Curie-Skłodowska, Sect. A 64, No. 1, 63-73 (2010). Summary: We consider a class of univalent orientation-preserving harmonic functions defined on the exterior of the unit disk which satisfy the condition \(\sum^{\infty}_{n=1} n^p (|a_n|+|b_n|) \leq 1\). We are interested in finding the radii of univalence and convexity for this class, and we find extremal functions. The convolutions, convex combinations, and explicit quasiconformal extensions for this class are also determined. MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) Keywords:harmonic function; quasiconformal extension; radius of convexity; radius of univalence PDFBibTeX XMLCite \textit{J. Widomski} and \textit{M. Gregorczyk}, Ann. Univ. Mariae Curie-Skłodowska, Sect. A 64, No. 1, 63--73 (2010; Zbl 1213.30042) Full Text: DOI Link