Harmonic shears of slit and polygonal mappings

Research output: Contribution to journalArticleScientificpeer-review


  • Saminathan Ponnusamy
  • Tri Quach
  • Antti Rasila

Research units

  • Indian Institute of Technology, Madras


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
Publication statusPublished - 1 Mar 2014
MoE publication typeA1 Journal article-refereed

    Research areas

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

ID: 9378551