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Harmonic mappings in the exterior of the unit disk

Jarosław Widomski;  Magdalena Gregorczyk — 2010

Annales UMCS, Mathematica

In this paper we consider a class of univalent orientation-preserving harmonic functions defined on the exterior of the unit disk which satisfy the condition [...] . We are interested in finding radius of univalence and convexity for such class and we find extremal functions. Convolution, convex combination, and explicit quasiconformal extension for this class are also determined.

Harmonic mappings in the exterior of the unit disk

Magdalena Gregorczyk;  Jarosław Widomski — 2010

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

In this paper we consider a class of univalent orientation-preserving harmonic functions defined on the exterior of the unit disk which satisfy the condition ∑ n = 1 ∞ n p ( | a n | + | b n | ) ≤ 1 . We are interested in finding radius of univalence and convexity for such class and we find extremal functions. Convolution, convex combination, and explicit quasiconformal extension for this class are also determined.

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