Harmonic shears of slit and polygonal mappings

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Harmonic shears of slit and polygonal mappings. / Ponnusamy, Saminathan; Quach, Tri; Rasila, Antti.

In: Applied Mathematics and Computation, Vol. 233, 01.03.2014, p. 588-598.

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Ponnusamy, Saminathan ; Quach, Tri ; Rasila, Antti. / Harmonic shears of slit and polygonal mappings. In: Applied Mathematics and Computation. 2014 ; Vol. 233. pp. 588-598.

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@article{0315ef079ef8423c8e46958ba073e3df,
title = "Harmonic shears of slit and polygonal mappings",
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 ω. 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 = "Convex along real directions, Convex functions, Harmonic shear, Harmonic univalent mappings, Minimal surfaces, Polygonal mappings, Slit mappings",
author = "Saminathan Ponnusamy and Tri Quach and Antti Rasila",
year = "2014",
month = "3",
day = "1",
doi = "10.1016/j.amc.2014.01.076",
language = "English",
volume = "233",
pages = "588--598",
journal = "Applied Mathematics and Computation",
issn = "0096-3003",
publisher = "Elsevier Inc.",

}

RIS - Download

TY - JOUR

T1 - Harmonic shears of slit and polygonal mappings

AU - Ponnusamy, Saminathan

AU - Quach, Tri

AU - Rasila, Antti

PY - 2014/3/1

Y1 - 2014/3/1

N2 - 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 ω. 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.

AB - 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 ω. 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.

KW - Convex along real directions

KW - Convex functions

KW - Harmonic shear

KW - Harmonic univalent mappings

KW - Minimal surfaces

KW - Polygonal mappings

KW - Slit mappings

UR - http://www.scopus.com/inward/record.url?scp=84896443046&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2014.01.076

DO - 10.1016/j.amc.2014.01.076

M3 - Article

VL - 233

SP - 588

EP - 598

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -

ID: 9378551