A note on renormalized volume functionals

2012/11/27 by Sun-Yung Alice Chang, Hao Fang, Chang, Sun-Yung Alice +3
Mathematics · #53C15 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG #msc:53C15

paper · pdf · doi:10.48550/arxiv.1211.6422

15 pages

arxiv created 2012/11/27 · arxiv updated 2012/11/28

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.

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