A Volume Comparison Theorem for Asymptotically Hyperbolic Manifolds

Simon Brendle; Otis Chodosh

doi:10.1007/s00220-014-2074-1

A Volume Comparison Theorem for Asymptotically Hyperbolic Manifolds

Simon Brendle, Otis Chodosh

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

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)
Pages (from-to)	839-846
Number of pages	8
Journal	Communications In Mathematical Physics
Volume	332
Issue number	2
DOIs	https://doi.org/10.1007/s00220-014-2074-1
State	Published - Dec 1 2014

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-014-2074-1

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title = "A Volume Comparison Theorem for Asymptotically Hyperbolic Manifolds",

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.",

author = "Simon Brendle and Otis Chodosh",

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AU - Chodosh, Otis

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AB - 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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EP - 846

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A Volume Comparison Theorem for Asymptotically Hyperbolic Manifolds

Abstract

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