Maximal slices in anti-de Sitter spaces

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概要

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• 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.

• 東北大学の論文

著者

• Shi Yuguang

  Key Laboratory Of Pure And Applied Mathematics School Of Mathematics Science Peking University

• Shi Yuguang

  Key Laboratory Of Pure And Applied Mathematics School Of Mathematical Science Peking University

• Li Zhenyang

  Key Laboratory of Pure and Applied Mathematics, School of Mathematics Science, Peking University

• Li Zhenyang

  Key Laboratory Of Pure And Applied Mathematics School Of Mathematics Science Peking University

関連論文

• A non-existence theorem of proper harmonic morphisms from weakly asymptotically hyperbolic manifolds
• Maximal slices in anti-de Sitter spaces

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