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A note on renormalized volume functionals
Journal article   Open access   Peer reviewed

A note on renormalized volume functionals

Sun-Yung Alice Chang, Hao Fang and C. Robin Graham
Differential geometry and its applications, Vol.33, pp.246-258
03/2014
DOI: 10.1016/j.difgeo.2013.10.001
url
https://doi.org/10.1016/j.difgeo.2013.10.001View
Published (Version of record) Open Access

Abstract

New properties are derived of renormalized volume functionals, which arise as coefficients in the asymptotic expansion of the volume of an asymptotically hyperbolic Einstein (AHE) manifold. A formula is given for the renormalized volume of an even-dimensional AHE manifold in terms of an arbitrary totally geodesic compactification. The second variation of renormalized volume functionals under conformal change is identified, and is used to show that Einstein metrics of nonzero scalar curvature are local extrema.
Renormalized volume functionals Asymptotically hyperbolic Einstein metric

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