Characterization of Large Isoperimetric Regions in Asymptotically Hyperbolic Initial Data

Otis Chodosh, Michael Eichmair, Yuguang Shi, Jintian Zhu

Research output: Contribution to journalArticle

Abstract

Let (M, g) be a complete Riemannian 3-manifold asymptotic to Schwarzschild-anti-deSitter and with scalar curvature R≥ - 6. Building on work of A. Neves and G. Tian and of the first-named author, we show that the leaves of the canonical foliation of (M, g) are the unique solutions of the isoperimetric problem for their area. The assumption R≥ - 6 is necessary. This is the first characterization result for large isoperimetric regions in the asymptotically hyperbolic setting that does not assume exact rotational symmetry at infinity.

Original languageEnglish (US)
Pages (from-to)777-798
Number of pages22
JournalCommunications In Mathematical Physics
Volume368
Issue number2
DOIs
StatePublished - Jun 1 2019

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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