On harmonic mappings lifting to minimal surfaces

TAŞTAN H. M., Polatoǧlu Y.

Mathematica, cilt.54, sa.77, ss.185-190, 2012 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 54 Sayı: 77
  • Basım Tarihi: 2012
  • Dergi Adı: Mathematica
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.185-190
  • Anahtar Kelimeler: Distortion theorem, Harmonic mapping, Isothermal parametrization, Minimal surface, Weierstrass-enneper representation
  • İstanbul Kültür Üniversitesi Adresli: Evet

Özet

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 *.