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.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 17, Differential and Functional Differential Equations. Part 3, 2006.
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Yang, P., Chang, S.Y.A. & Qing, J. On the renormalized volumes for conformally compact Einstein manifolds. J Math Sci 149, 1755–1769 (2008). https://doi.org/10.1007/s10958-008-0094-0
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DOI: https://doi.org/10.1007/s10958-008-0094-0