On harmonic mappings lifting to minimal surfaces

TAŞTAN H. M., Polatoǧlu Y.

Mathematica, vol.54, no.77, pp.185-190, 2012 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 77
  • Publication Date: 2012
  • Journal Name: Mathematica
  • Journal Indexes: Scopus
  • Page Numbers: pp.185-190
  • Keywords: Distortion theorem, Harmonic mapping, Isothermal parametrization, Minimal surface, Weierstrass-enneper representation
  • Istanbul Kültür University Affiliated: Yes

Abstract

The projection on the base plane of a regular minimal surface S in ℝ 3 with isothermal parameters defines a complex-valued univalent harmonic function f. We obtain distortion theorems for the Weierstrass-Enneper parameters and the Gaussian curvature of the minimal surface S, provided that the corresponding univalent harmonic function f belongs to the class S H *.