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L^2 curvature and volume renormalization of AHE metrics on 4-manifolds
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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.
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Boundary Curvature Scalars on Conformally Compact Manifolds
Five CC boundary curvature scalars are constructed explicitly, yielding conformal invariants, singular Yamabe expansion coefficients, and Dirichlet-to-Neumann maps.
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