Harmonic Shears and Numerical Conformal Mappings

Quach, Tri

doi:10.48550/arxiv.1405.6759

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Theorem B (Weierstrass-enneper Representation)1

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2019

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“…Further information about the relationship between certain harmonic mappings and the associated minimal surfaces can be found from [2,4,[9][10][11][12]. In [7], the authors considered for example the single slit CHD mapping, namely, the Koebe function k(z) = z/(1 − z) 2 , and derived the following result.…”

Section: Theorem B (Weierstrass-enneper Representation)mentioning

confidence: 99%

Univalent Harmonic Mappings and Lift to the Minimal Surfaces

Liu

Ponnusamy

2019

Lobachevskii J Math

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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 Mathematica software.2010 Mathematics Subject Classification. 30C65, 30C45.

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