Harmonic shears of slit and polygonal mappings

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School of Science | D4 Julkaistu kehittämis- tai tutkimusraportti tai -selvitys
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Date

2012

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Matematiikan ja systeemianalyysin laitos
Department of Mathematics and Systems Analysis

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en

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21

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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.

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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

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https://urn.fi/URN:ISBN:978-952-60-4520-7

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[report] Perustieteiden korkeakoulu / SCI