2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106259We 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.21 pagesDifferential GeometryMathematical Physics53C21, 58J50text