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Harmonic mappings in the exterior of the unit disk. (English) Zbl 1213.30042

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.)
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