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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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説明
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.
収録刊行物
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- Ｔｏｈｏｋｕ Ｍａｔｈｅｍａｔｉｃａｌ Ｊｏｕｒｎａｌ， Ｓｅｃｏｎｄ Ｓｅｒｉｅｓ
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Ｔｏｈｏｋｕ Ｍａｔｈｅｍａｔｉｃａｌ Ｊｏｕｒｎａｌ， Ｓｅｃｏｎｄ Ｓｅｒｉｅｓ 60 (2), 253-265, 2008
東北大学大学院理学研究科数学専攻
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詳細情報 詳細情報について
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- CRID
- 1390282680095785600
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- NII論文ID
- 130001073234
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- ISSN
- 2186585X
- 00408735
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- MRID
- 2428863
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- 本文言語コード
- en
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- データソース種別
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- JaLC
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