On the renormalized volumes for conformally compact Einstein manifolds
arXiv:math/0512376
Abstract
We study the renormalized volume of a conformally compact Einstein manifold. In even dimensions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the dimension is odd, we relate the renormalized volume to the conformal primitive of the -curvature. We show how all the global information come from the Scattering.
21 pages
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