Renormalizing Curvature Integrals on Poincare-Einstein Manifolds

Abstract

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.

References in corpus (4)

• Homology of pseudodifferential operators I. Manifolds with boundary
• Topics in conformally compact Einstein metrics
• Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds
• Meromorphic properties of the resolvent on asymptotically hyperbolic manifolds

Cited by in corpus (1)

• Renormalized area and properly embedded minimal surfaces in hyperbolic 3-manifolds