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arXiv · 1305.6628

A volume comparison theorem for asymptotically hyperbolic manifolds

S. Brendle·O. Chodosh
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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.

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S. Brendle, O. Chodosh. 2013-05-28. A volume comparison theorem for asymptotically hyperbolic manifolds. https://doi.org/10.1007/s00220-014-2074-1

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