On the renormalized volumes for conformally compact Einstein manifolds

Details On the renormalized volumes for conformally compact Einstein manifolds On the renormalized volumes for conformally compact Einstein manifolds

2005-12-15

arxiv.org/abs/math/0512376v2

Mathematics

Differential Geometry

21 pages

Scientific paper

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 $Q$-curvature. We show
how all the global information come from the Scattering.

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