Email this article Univalent Harmonic Mappings and Lift to the Minimal Surfaces
- Authors: Jiang Y.P.1, Liu Z.2, Ponnusamy S.3
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Affiliations:
- School of Mathematics and Econometrics
- College of Science
- Department of Mathematics
- Issue: Vol 40, No 9 (2019)
- Pages: 1295-1312
- Section: Article
- URL: https://bakhtiniada.ru/1995-0802/article/view/205470
- DOI: https://doi.org/10.1134/S1995080219090099
- ID: 205470
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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. In several of the cases, we illustrate mappings together with their minimal surfaces pictorially with the help of Mathematica software.
About the authors
Yue Ping Jiang
School of Mathematics and Econometrics
Author for correspondence.
Email: ypjiang731@163.com
China, Changsha, Hunan, 410082
Zhihong Liu
College of Science
Author for correspondence.
Email: liuzhihongmath@163.com
China, Guilin, Guangxi, 541004
Saminathan Ponnusamy
Department of Mathematics
Author for correspondence.
Email: samy@iitm.ac.in
India, Chennai, 600 036
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