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2008 Maximal slices in anti-de Sitter spaces
Zhenyang Li, Yuguang Shi
Tohoku Math. J. (2) 60(2): 253-265 (2008). DOI: 10.2748/tmj/1215442874

Abstract

We prove the existence of maximal slices in anti-de Sitter spaces (ADS spaces) with small boundary data at spatial infinity. The main argument is carried out by implicit function theorem. We also get a necessary and sufficient condition for the boundary behavior of totally geodesic slices in ADS spaces. Moreover, we show that any isometric and maximal embedding of hyperbolic spaces into ADS spaces must be totally geodesic. Combined with this, we see that most of maximal slices obtained in this paper are not isometric to hyperbolic spaces, which implies that the Bernstein Theorem in ADS space fails.

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Zhenyang Li. Yuguang Shi. "Maximal slices in anti-de Sitter spaces." Tohoku Math. J. (2) 60 (2) 253 - 265, 2008. https://doi.org/10.2748/tmj/1215442874

Information

Published: 2008
First available in Project Euclid: 7 July 2008

zbMATH: 1203.53068
MathSciNet: MR2428863
Digital Object Identifier: 10.2748/tmj/1215442874

Subjects:
Primary: 53C50
Secondary: 58J32

Rights: Copyright © 2008 Tohoku University

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Vol.60 • No. 2 • 2008
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