A Volume Comparison Theorem for Asymptotically Hyperbolic Manifolds

Simon Brendle, Otis Chodosh

Research output: Contribution to journalArticle

7 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 languageEnglish (US)
Pages (from-to)839-846
Number of pages8
JournalCommunications In Mathematical Physics
Volume332
Issue number2
DOIs
StatePublished - Dec 1 2014

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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