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Univalent harmonic mappings and lift to the minimal surfaces

We construct sense-preserving univalent harmonic mappings which map the unit disk onto a domain which is convex in the horizontal direction, but with varying dilatation. Also, we obtain minimal surfaces associated with such harmonic mappings. This solves also a recent problem of Dorff and Muir (Abstr. Appl. Anal. (2014)). In several of the cases, we illustrate mappings together with their minimal surfaces pictorially with the help of \texttt{Mathematica} software.

preprint2015arXivOpen access
Yueping JiangZhihong LiuSaminathan Ponnusamy
math.CV
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Open access3 authors1 topic
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Yueping JiangZhihong LiuSaminathan Ponnusamy

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