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Zbl 1152.53006
Espinar, José M.
A Plateau problem for complete surfaces in the de Sitter three-space. (English)
[A] Mladenov, Iva\"ilo (ed.) et al., Proceedings of the 8th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 9--14, 2006. Sofia: Bulgarian Academy of Sciences. 156-168 (2007). ISBN 978-954-8495-37-0/pbk

In this paper, the author establishes some existence and uniqueness theorems for a Plateau problem at infinity for complete space-like surfaces in the de Sitter 3-space $S^3_1$ whose mean curvature $H$ and Gauss curvature $K$ verify the linear relationship $2\varepsilon (H-1)-(\varepsilon +1)(K-1)-0$ for $-\varepsilon\in R^{+}$. The Plateau problem considered in this paper is as follows: Given $\varepsilon_0<0$ and a Jordan curve $\Gamma $ on $S^2_{\infty}\equiv\Pi\cup\{\infty\}$, find a complete BLW-surface $\psi :S\to S^3_1$ verifying $2\varepsilon_0(H-1)-(\varepsilon_0+1)(K-1)=0$ and such that $\Gamma$ is its asymptotic boundary.
[Shen Yi-Bing (Hangzhou)]

MSC 2000:: *53A10 Minimal surfaces, surfaces with prescribed mean curvature
53A35 Non-Euclidean differential geometry

Keywords: Plateau problem; de Sitter space; space-like surface; Gauss curvature

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