Journals / Turkish Journal of Mathematics / 2013 / Cilt: 37 - Sayı: 2
On quasiconformal harmonic mappings lifting to minimal surfaces
- Pages
- 267–277
- DOI
- —
Abstract
We prove a growth theorem for a function to belong to the class \sum(m;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 L3. We also obtain some estimates of the Gaussian curvature of the minimal surfaces in 3-dimensional Euclidean space R3 and of the spacelike minimal surfaces in L3.
Özet
We prove a growth theorem for a function to belong to the class \sum(m;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 L3. We also obtain some estimates of the Gaussian curvature of the minimal surfaces in 3-dimensional Euclidean space R3 and of the spacelike minimal surfaces in L3.