A Note on Renormalized Volume Functionals
نویسندگان
چکیده
The asymptotic expansion of the volume of an asymptotically hyperbolic Einstein (AHE) metric defines invariants of the AHE metric and of a metric in the induced conformal class at infinity. These have been of recent interest, motivated in part by the AdS/CFT correspondence in physics. In this paper we derive some new properties of these invariants. Let (X, g+) be AHE with smooth conformal infinity (M, [g]), M = ∂X. We always assume that X is connected although ∂X need not be. If r is a geodesic defining function associated to a metric g in the conformal class at infinity (see §2 for more details), we have the following volume expansion ([G1]):
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