  We discuss the AdS/CFT correspondence for negative curvature Einstein
manifolds whose conformal boundary is degenerate in the sense that it is of
codimension greater than one. In such manifolds, hypersurfaces of constant
radius do not blow up uniformly as one increases the radius; examples include
products of hyperbolic spaces and the Bergman metric. We find that there is a
well-defined correspondence between the IR regulated bulk theory and conformal
field theory defined in a background whose degenerate geometry is regulated by
the same parameter. We are hence able to make sense of supergravity in
backgrounds such as $AdS_{3} \times H^{2}$.
