Harmonic close-to-convex functions and minimal surfaces

Saminathan Ponnusamy, Antti Rasila*, A. Sairam Kaliraj

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

In this paper, we study the family of sense-preserving complex-valued harmonic functions that are normalized close-to-convex functions on the open unit disk with. We derive a sufficient condition for to belong to the class. We take the analytic part of to be or and for a suitable choice of co-analytic part of, the second complex dilatation turns out to be a square of an analytic function. Hence, is lifted to a minimal surface expressed by an isothermal parameter. Explicit representation for classes of minimal surfaces are given. Graphs generated by using Mathematica are used for illustration.

Original languageEnglish
Pages (from-to)986-1002
Number of pages17
JournalComplex Variables and Elliptic Equations
Volume59
Issue number7
DOIs
StatePublished - Jul 2014

Keywords

  • Gaussian hypergeometric functions
  • close-to-convex
  • coefficient inequality
  • convex in vertical direction
  • minimal surfaces
  • univalence
  • univalent harmonic functions

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