Harmonic shears of slit and polygonal mappings

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

Tutkijat

  • Saminathan Ponnusamy
  • Tri Quach
  • Antti Rasila

Organisaatiot

  • Indian Institute of Technology, Madras

Kuvaus

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.

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut588-598
Sivumäärä11
JulkaisuApplied Mathematics and Computation
Vuosikerta233
TilaJulkaistu - 1 maaliskuuta 2014
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

ID: 9378551