L-2 curvature and volume renormalization of AHE metrics on 4-manifolds

This paper relates the boundary term in the Chern-Gauss-Bonnet formula on 4 -manifolds M with the renormalized volume V, as defined in the AdS/CFT corr espondence, for asymptotically hyperbolic Einstein metrics on M. In additio n rye compute and discuss the differential or Variation dV of V, or equival ently the variation of the L-2 norm of the Weyl curvature, on the space of such Einstein metrics.