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|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. (C) 2013 Elsevier B.V. All rights reserved.|
|Electronic Publication Date:||22-Nov-2013|
|Citation:||Chang, Sun-Yung Alice, Fang, Hao, Graham, C Robin. (2014). A note on renormalized volume functionals. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 33 (246 - 258. doi:10.1016/j.difgeo.2013.10.001|
|Pages:||246 - 258|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS|
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