On quasiconformal harmonic mappings lifting to minimal surfaces

Authors

HAKAN METE TAŞTAN
YAŞAR POLATOĞLU

DOI

10.3906/mat-1106-36

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.

Keywords

Minimal surface, isothermal parameters, Weierstrass-Enneper representation, quasiconformal harmonic mapping

First Page

267

Last Page

277

Recommended Citation

TAŞTAN, HAKAN METE and POLATOĞLU, YAŞAR (2013) "On quasiconformal harmonic mappings lifting to minimal surfaces," Turkish Journal of Mathematics: Vol. 37: No. 2, Article 8. https://doi.org/10.3906/mat-1106-36
Available at: https://journals.tubitak.gov.tr/math/vol37/iss2/8