Univalent harmonic mappings and lift to the minimal surfaces
Complex Variables
2015-08-04 v1
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.
Keywords
Cite
@article{arxiv.1508.00199,
title = {Univalent harmonic mappings and lift to the minimal surfaces},
author = {YuePing Jiang and ZhiHong Liu and Saminathan Ponnusamy},
journal= {arXiv preprint arXiv:1508.00199},
year = {2015}
}
Comments
24 pages with many figures