Renormalizing Curvature Integrals on Poincare-Einstein Manifolds
Differential Geometry
2010-12-30 v1
Abstract
After analyzing renormalization schemes on a Poincar\'e-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 Poincar\'e-Einstein structure, and obtain, from the renormalized integral of the Pfaffian, an extension of the Gauss-Bonnet theorem.
Cite
@article{arxiv.math/0504161,
title = {Renormalizing Curvature Integrals on Poincare-Einstein Manifolds},
author = {Pierre Albin},
journal= {arXiv preprint arXiv:math/0504161},
year = {2010}
}