Characterization of Large Isoperimetric Regions in Asymptotically Hyperbolic Initial Data

Otis Chodosh (Korresp. Autor*in), Michael Eichmair, Yuguang Shi, Jintian Zhu

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

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.
OriginalspracheEnglisch
Seiten (von - bis)777 - 798
Seitenumfang22
FachzeitschriftCommunications in Mathematical Physics
Jahrgang368
Ausgabenummer2
DOIs
PublikationsstatusVeröffentlicht - Juni 2019

ÖFOS 2012

  • 101006 Differentialgeometrie
  • 103028 Relativitätstheorie

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