## Proceedings of the International Conference on Geometry, Integrability and Quantization

### A Plateau Problem for Complete Surfaces in the de-Sitter Three-Space

José M. Espinar

#### Abstract

In this paper we establish some existence and uniqueness theorems for a Plateau problem at infinity for complete spacelike surfaces in $S^{3}_{1}$ whose mean and Gauss–Kronecker curvatures verify the linear relationship $2 \varepsilon (H − 1) − (\varepsilon + 1)(K − 1) = 0$ for $− \varepsilon \in \mathbb{R}^+$.

#### Article information

Dates
First available in Project Euclid: 13 July 2015

https://projecteuclid.org/ euclid.pgiq/1436792826

Digital Object Identifier
doi:10.7546/giq-8-2007-156-168

Mathematical Reviews number (MathSciNet)
MR2341201

Zentralblatt MATH identifier
1152.53006

#### Citation

Espinar, José M. A Plateau Problem for Complete Surfaces in the de-Sitter Three-Space. Proceedings of the Eighth International Conference on Geometry, Integrability and Quantization, 156--168, Softex, Sofia, Bulgaria, 2007. doi:10.7546/giq-8-2007-156-168. https://projecteuclid.org/euclid.pgiq/1436792826