On quasiconformal harmonic mappings lifting to minimal surfaces


Tastan H. M. , Polatoglu Y.

TURKISH JOURNAL OF MATHEMATICS, vol.37, no.2, pp.267-277, 2013 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 2
  • Publication Date: 2013
  • Doi Number: 10.3906/mat-1106-36
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.267-277

Abstract

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 $\mathbb{L}^{3}.$

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.