Harmonic Shears of Slit and Polygonal Mappings
Complex Variables
2014-06-18 v1
Abstract
In this paper, we study harmonic mappings by using the shear construction, introduced by Clunie and Sheil-Small in 1984. We consider two classes of conformal mappings, each of which maps the unit disk D univalently onto a domain which is convex in the horizontal direction, and shear these mappings with suitable dilatations \omega. Mappings of the first class map the unit disk D onto four-slit domains and mappings of the second class take D onto regular n-gons. In addition, we discuss the minimal surfaces associated with such harmonic mappings. Furthermore, illustrations of mappings and associated minimal surfaces are given by using Mathematica.
Keywords
Cite
@article{arxiv.1201.2015,
title = {Harmonic Shears of Slit and Polygonal Mappings},
author = {Saminathan Ponnusamy and Tri Quach and Antti Rasila},
journal= {arXiv preprint arXiv:1201.2015},
year = {2014}
}
Comments
17 pages, 6 figures, 2 tables