On quasiconformal harmonic mappings lifting to minimal surfaces


Tastan H. M. , Polatoglu Y.

TURKISH JOURNAL OF MATHEMATICS, cilt.37, sa.2, ss.267-277, 2013 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 37 Konu: 2
  • Basım Tarihi: 2013
  • Doi Numarası: 10.3906/mat-1106-36
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Sayfa Sayıları: ss.267-277

Özet

We prove a growth theorem for a function to belong to the class Sigma(mu; a) and generalize a Weierstrass-Enneper representation type theorem for the minimal surfaces given in [5] to spacelike minimal surfaces which lie in 3-dimensional Lorentz-Minkowski space L-3. We also obtain some estimates of the Gaussian curvature of. the minimal surfaces in 3-dimensional Euclidean space R-3 and of the spacelike minimal surfaces in L-3.

We prove a growth theorem for a function to belong to the class $\sum(\mu;a)$ and
generalize a Weierstrass-Enneper representation type theorem for the minimal surfaces
given in \cite{Dure} to spacelike minimal surfaces which lie in 3-dimensional Lorentz-Minkowski space
$\mathbb{L}^{3}.$ We also obtain some estimates of the Gaussian curvature of the minimal surfaces in
3-dimensional Euclidean space $\mathbb{R}^{3}$ and of the spacelike minimal surfaces in $\mathbb{L}^{3}.$