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In the standard AdS/CFT, the conformally compactified Euclidean space is the conformal boundary of the bulk Euclidean AdS space. Are there any other Einstein spaces (with different topology) that takes the compactified Euclidean space as its conformal infinity? In other words, for the Dirichlet boundary value problem of the asymptotic hyperbolic Einstein metrics, are there other solutions with different topology?

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