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09 February 2025
 
  » arxiv » 1508.0199

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Univalent harmonic mappings and lift to the minimal surfaces
YuePing Jiang ; ZhiHong Liu ; Saminathan Ponnusamy ;
Date 2 Aug 2015
AbstractWe 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 exttt{Mathematica} software.
Source arXiv, 1508.0199
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