Journal article
A note on renormalized volume functionals
Differential geometry and its applications, Vol.33, pp.246-258
03/2014
DOI: 10.1016/j.difgeo.2013.10.001
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.
Details
- Title: Subtitle
- A note on renormalized volume functionals
- Creators
- Sun-Yung Alice Chang - Department of Mathematics, Princeton University, Princeton, NJ 08544, United StatesHao Fang - Department of Mathematics, University of Iowa, Maclean Hall, Iowa City, IA 52242-1419, United StatesC. Robin Graham - Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195-4350, United States
- Resource Type
- Journal article
- Publication Details
- Differential geometry and its applications, Vol.33, pp.246-258
- DOI
- 10.1016/j.difgeo.2013.10.001
- ISSN
- 0926-2245
- eISSN
- 1872-6984
- Publisher
- Elsevier B.V
- Grant note
- DMS-1008249 / NSF DMS-1308266 / NSF DMS-1104536 / NSF
- Language
- English
- Date published
- 03/2014
- Academic Unit
- Mathematics
- Record Identifier
- 9983985868102771
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