On harmonic mappings lifting to minimal surfaces
Mathematica, vol.54, no.77, pp.185-190, 2012 (Scopus)
- 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 *.