Maximal Slice in Anti-de Sitter Space

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dc.creatorLi, ZhenYang
dc.creatorshi, YuGuang
dc.date2006-09-11
dc.date.accessioned2026-07-07T07:24:42Z
dc.date.available2026-07-07T07:24:42Z
dc.descriptionIn this paper, we prove the existence of maximal slices in anti-de Sitter spaces (ADS spaces) with small boundary data at spatial infinity. The main arguments is implicit function theorem. We also get a necessary and sufficient condition for boundary behavior of totally geodesic slice in ADS space. Moreover, we show that any isometric and maximal embedding of hyperbolic spaces into ADS space must be totally geodesic. Together with this, we see that most of maximal slices we get in this paper are not isometric to hyperbolic spaces, which implies that the Bernstein Theorem in ADS space fails.
dc.description16pages
dc.identifierhttps://arxiv.org/abs/math/0609278
dc.identifierhttp://arxiv.org/abs/math/0609278
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/116462
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subject53C50 ; 58J32
dc.titleMaximal Slice in Anti-de Sitter Space
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