Large Isoperimetric Regions in Asymptotically Hyperbolic Manifolds

Otis Chodosh

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

We show the existence of isoperimetric regions of sufficiently large volumes in general asymptotically hyperbolic three manifolds. Furthermore, we show that large coordinate spheres are uniquely isoperimetric in manifolds that are Schwarzschild–anti-deSitter at infinity. These results have important repercussions for our understanding of spacelike hypersurfaces in Lorentzian space-times which are asymptotic to null infinity. In fact, as an application of our results, we verify the asymptotically hyperbolic Penrose inequality in the special case of the existence of connected isoperimetric regions of all volumes.

Original languageEnglish (US)
Pages (from-to)393-443
Number of pages51
JournalCommunications In Mathematical Physics
Volume343
Issue number2
DOIs
StatePublished - Apr 1 2016

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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