Renormalizing Curvature Integrals on PoincareEinstein Manifolds
Abstract
After analyzing renormalization schemes on a PoincaréEinstein manifold, we study the renormalized integrals of scalar Riemannian invariants. The behavior of the renormalized volume is wellknown, and we show any scalar Riemannian invariant renormalizes similarly. We consider characteristic forms and their behavior under a variation of the PoincaréEinstein structure, and obtain, from the renormalized integral of the Pfaffian, an extension of the GaussBonnet theorem.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2005
 DOI:
 10.48550/arXiv.math/0504161
 arXiv:
 arXiv:math/0504161
 Bibcode:
 2005math......4161A
 Keywords:

 Mathematics  Differential Geometry;
 53B20
 EPrint:
 Advances in Mathematics, Volume 221, Issue 1, 1 May 2009, Pages 140169