  We study the asymptotic behavior of the bulk spacetimes with the negative
cosmological constant in the context of the brane-world scenario. We show that,
in Euclidean bulk, or in Lorentzian static bulk, some sequences of
hypersurfaces with the positive Ricci scalar evolve to the warped geometries
like the anti-de Sitter spacetime. Based on the AdS/CFT correspondence, we
discuss that the positivity of the Ricci scalar is related to the stability of
CFT on the brane. In addition, the brane-world is described from the
holographic point of view. The asymptotic local structure of the conformal
infinity is also investigated.
