Geodesic
On the renormalized volumes for conformally compact Einstein manifolds
Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 3, Tome 17 (2006), pp. 129-142.

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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. 
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P. Yang; J. Qing; S.-Yu. Chang. On the renormalized volumes for conformally compact Einstein manifolds. Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 3, Tome 17 (2006), pp. 129-142. http://geodesic.mathdoc.fr/item/CMFD_2006_17_a8/

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