Harmonic shears of slit and polygonal mappings

Saminathan Ponnusamy, Tri Quach*, Antti Rasila

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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.

Original languageEnglish
Pages (from-to)588-598
Number of pages11
JournalApplied Mathematics and Computation
StatePublished - 1 Mar 2014
Externally publishedYes


  • Convex along real directions
  • Convex functions
  • Harmonic shear
  • Harmonic univalent mappings
  • Minimal surfaces
  • Polygonal mappings
  • Slit mappings


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