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MAXIMAL SLICES IN ANTI-DE SITTER SPACES
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- LI ZHENYANG
- Key Laboratory of Pure, and Applied mathematics, School of Mathematics Science, Peking University
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- SHI YUGUANG
- Key Laboratory of Pure, and Applied mathematics, School of Mathematics Science, Peking University
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Description
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.
Journal
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- Tohoku Mathematical Journal, Second Series
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Tohoku Mathematical Journal, Second Series 60 (2), 253-265, 2008
Mathematical Institute, Tohoku University
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Details 詳細情報について
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- CRID
- 1390282680095785600
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- NII Article ID
- 130001073234
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- ISSN
- 2186585X
- 00408735
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- MRID
- 2428863
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- Text Lang
- en
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- Data Source
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- JaLC
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed