On the renormalized volumes for conformally compact Einstein manifolds

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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.

Original languageEnglish (US)
Pages (from-to)1755-1769
Number of pages15
JournalJournal of Mathematical Sciences
Volume149
Issue number6
DOIs
StatePublished - Mar 1 2008

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

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