TY - JOUR
T1 - Renormalizing curvature integrals on Poincaré-Einstein manifolds
AU - Albin, Pierre
N1 - Funding Information:
This work forms part of my thesis. I am very grateful to my advisor, Rafe Mazzeo, for sharing his great erudition and insight. Throughout this work, I received support from his NSF grant DMS-0204730. I would like to thank Tom Branson for his invitation to participate in the conformal geometry program at the Erwin Schrödinger Institute in Vienna in spring of 2004. I was fortunate to coincide there with him and Robin Graham, and I would like to thank them both for very interesting conversations. I am grateful to the anonymous referee for many helpful comments. I am also grateful to the ETH in Zürich for its hospitality during the summer semester of 2004, and to the Starbucks branches in Zürich and Palo Alto where most of this work was carried out.
PY - 2009/5/1
Y1 - 2009/5/1
N2 - 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.
AB - 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.
KW - Asymptotically hyperbolic Einstein metrics
KW - Gauss-Bonnet theorem
KW - Lipschitz-Killing curvature
KW - Renormalization schemes
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U2 - 10.1016/j.aim.2008.12.002
DO - 10.1016/j.aim.2008.12.002
M3 - Article
AN - SCOPUS:62249214209
SN - 0001-8708
VL - 221
SP - 140
EP - 169
JO - Advances in Mathematics
JF - Advances in Mathematics
IS - 1
ER -