On the renormalized volumes for conformally compact Einstein manifolds

Research paper by P. Yang, S. -Yu. A. Chang, J. Qing

Indexed on: 01 Mar '08Published on: 01 Mar '08Published in: Journal of Mathematical Sciences


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.