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arXiv · 1201.2015

Harmonic Shears of Slit and Polygonal Mappings

Saminathan Ponnusamy·Tri Quach·Antti Rasila
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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.

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BibTeXRIS

Saminathan Ponnusamy, Tri Quach, Antti Rasila. 2012-01-10. Harmonic Shears of Slit and Polygonal Mappings. https://doi.org/10.1016/j.amc.2014.01.076

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