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We study the asymptotic behavior of the bulk spacetimes with the negativecosmological constant in the context of the brane-world scenario. We show that,in Euclidean bulk, or in Lorentzian static bulk, some sequences ofhypersurfaces with the positive Ricci scalar evolve to the warped geometrieslike the anti-de Sitter spacetime. Based on the AdS/CFT correspondence, wediscuss that the positivity of the Ricci scalar is related to the stability ofCFT on the brane. In addition, the brane-world is described from theholographic point of view. The asymptotic local structure of the conformalinfinity is also investigated.Comment: 6 pages, minor changes, to appear in Phys. Rev.

Anti–de Sitter no-hair, AdS/CFT and the brane-world