### 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.

Original language | English (US) |
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Pages (from-to) | 839-846 |

Number of pages | 8 |

Journal | Communications In Mathematical Physics |

Volume | 332 |

Issue number | 2 |

DOIs | |

State | Published - Dec 1 2014 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Brendle, S., & Chodosh, O. (2014). A Volume Comparison Theorem for Asymptotically Hyperbolic Manifolds.

*Communications In Mathematical Physics*,*332*(2), 839-846. https://doi.org/10.1007/s00220-014-2074-1