Renormalizing curvature integrals on Poincaré-Einstein manifolds

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After analyzing renormalization schemes on a Poincaré-Einstein manifold, we study the renormalized integrals of scalar Riemannian invariants. The behavior of the renormalized volume is well known and we show any scalar Riemannian invariant renormalizes similarly. We consider characteristic forms and their behavior under a variation of the Poincaré-Einstein structure and obtain, from the renormalized integral of the Pfaffian, an extension of the Gauss-Bonnet theorem.

Original languageEnglish (US)
Pages (from-to)140-169
Number of pages30
JournalAdvances in Mathematics
Issue number1
StatePublished - May 1 2009
Externally publishedYes


  • Asymptotically hyperbolic Einstein metrics
  • Gauss-Bonnet theorem
  • Lipschitz-Killing curvature
  • Renormalization schemes

ASJC Scopus subject areas

  • Mathematics(all)


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