L^2 curvature and volume renormalization of AHE metrics on 4-manifolds
Differential Geometry
2007-05-23 v2
Abstract
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.
Keywords
Cite
@article{arxiv.math/0011051,
title = {L^2 curvature and volume renormalization of AHE metrics on 4-manifolds},
author = {Michael T. Anderson},
journal= {arXiv preprint arXiv:math/0011051},
year = {2007}
}
Comments
15 pages, several corrections made. To appear in Math. Research Letters