On quasiconformal harmonic mappings lifting to minimal surfaces

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 [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.