Harmonic shears of slit and polygonal mappings
Loading...
Journal Title
Journal ISSN
Volume Title
School of Science |
D4 Julkaistu kehittämis- tai tutkimusraportti tai -selvitys
Unless otherwise stated, all rights belong to the author. You may download, display and print this publication for Your own personal use. Commercial use is prohibited.
Date
2012
Major/Subject
Mcode
Degree programme
Language
en
Pages
21
Series
Aalto University publication series SCIENCE+TECHNOLOGY, 3/2012
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 !. 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.Description
Keywords
harmonic univalent mappings, convex along wear directions, convex functions, harmonic shear, polygonal mappings, slit mappings, minimal surfaces, AMS:30C99, AMS:30C62, AMS:31A62, AMS:53A10
