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Abstract: The first author proved that the harmonic convolution of a normalized righthalf-plane mapping with either another normalized right half-plane mapping or anormalized vertical strip mapping is convex in the direction of the real axis.provided that it is locally univalent.
In this paper, we prove that in generalthe assumption of local univalency cannot be omitted.
However, we are able toshow that in some cases these harmonic convolutions are locally univalent.Using this we obtain interesting examples of univalent harmonic maps one ofwhich is a map onto the plane with two parallel slits.



Author: Michael Dorff, Maria Nowak, Magdalena Woloszkiewicz

Source: https://arxiv.org/



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