Maximal Slice in Anti-de Sitter Space

Details Maximal Slice in Anti-de Sitter Space Maximal Slice in Anti-de Sitter Space

2006-09-11

arxiv.org/abs/math/0609278v1

Mathematics

Differential Geometry

16pages

Scientific paper

In 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.

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