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On the renormalized volumes for conformally compact Einstein manifolds

Alice Chang·Jie Qing·Paul Yang
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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 $Q$-curvature. We show how all the global information come from the Scattering.

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Alice Chang, Jie Qing, Paul Yang. 2005-12-20. On the renormalized volumes for conformally compact Einstein manifolds. https://arxiv.org/abs/math/0512376

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