## On quasiconformal harmonic mappings lifting to minimal surfaces

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

• 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.