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A note on renormalized volume functionals

Author(s): Chang, Sun-Yung A.; Fang, Hao; Graham, C Robin

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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.
Publication Date: Mar-2014
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
DOI: doi:10.1016/j.difgeo.2013.10.001
ISSN: 0926-2245
EISSN: 1872-6984
Pages: 246 - 258
Type of Material: Journal Article
Version: Author's manuscript

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