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arXiv · 1508.00199

Univalent harmonic mappings and lift to the minimal surfaces

YuePing Jiang·ZhiHong Liu·Saminathan Ponnusamy
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Abstract

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.

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YuePing Jiang, ZhiHong Liu, Saminathan Ponnusamy. 2015-08-02. Univalent harmonic mappings and lift to the minimal surfaces. https://arxiv.org/abs/1508.00199

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