A volume comparison theorem for asymptotically hyperbolic manifolds
Differential Geometry
2015-06-16 v1
Abstract
We define a notion of renormalized volume of an asymptotically hyperbolic manifold. Moreover, we prove a sharp volume comparison theorem for metrics with scalar curvature at least -6. Finally, we show that the inequality is strict unless the metric is isometric to one of the Anti-deSitter-Schwarzschild metrics.
Cite
@article{arxiv.1305.6628,
title = {A volume comparison theorem for asymptotically hyperbolic manifolds},
author = {S. Brendle and O. Chodosh},
journal= {arXiv preprint arXiv:1305.6628},
year = {2015}
}