| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4605942 | Differential Geometry and its Applications | 2014 | 13 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Sun-Yung Alice Chang, Hao Fang, C. Robin Graham,