  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
correspondence, for asymptotically hyperbolic Einstein metrics on M. In
addition, we compute and discuss the differential or variation dV of V, or
equivalently the variation of the L^2 norm of the Weyl curvature, on the space
of such Einstein metrics.

Differential Geometry