Characterization of Large Isoperimetric Regions in Asymptotically Hyperbolic Initial Data

Otis Chodosh; Michael Eichmair; Yuguang Shi; Jintian Zhu

doi:10.1007/s00220-019-03354-2

Characterization of Large Isoperimetric Regions in Asymptotically Hyperbolic Initial Data

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

Institut für Mathematik

Veröffentlichungen: Beitrag in Fachzeitschrift › Artikel › Peer 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.

Originalsprache	Englisch
Seiten (von - bis)	777 - 798
Seitenumfang	22
Fachzeitschrift	Communications in Mathematical Physics
Jahrgang	368
Ausgabenummer	2
DOIs	https://doi.org/10.1007/s00220-019-03354-2
Publikationsstatus	Veröffentlicht - Juni 2019

Fördermittel

Acknowledgements. Open access funding provided by Austrian Science Fund (FWF). O. Chodosh is supported by the Oswald Veblen Fund and the NSF grants No. 1638352 and 1811059. M. Eichmair is supported by the START-Project Y963-N35 of the Austrian Science Fund (FWF). O. Chodosh and M. Eichmair thank the Erwin Schr\u00F6dinger Institute for its warm hospitality during the program Geometry and Relativity in the Summer of 2017. They also thank Professors Hubert Bray, Simon Brendle, Gerhard Huisken, Jan Metzger, Richard Schoen, and Paul Yang for their kind support and encouragement. Y. Shi and J. Zhu are supported by the NSFC grants No. 11671015 and 11731001. They would like thank Professor Li Yuxiang for his kind support. Open access funding provided by Austrian Science Fund (FWF). O. Chodosh is supported by the Oswald Veblen Fund and the NSF grants No. 1638352 and 1811059. M. Eichmair is supported by the START-Project Y963-N35 of the Austrian Science Fund (FWF). O. Chodosh and M. Eichmair thank the Erwin Schr?dinger Institute for its warm hospitality during the program Geometry and Relativity in the Summer of 2017. They also thank Professors Hubert Bray, Simon Brendle, Gerhard Huisken, Jan Metzger, Richard Schoen, and Paul Yang for their kind support and encouragement. Y. Shi and J. Zhu are supported by the NSFC grants No. 11671015 and 11731001. They would like thank Professor Li Yuxiang for his kind support.

ÖFOS 2012

101006 Differentialgeometrie
103028 Relativitätstheorie

Zugriff auf Dokument

10.1007/s00220-019-03354-2Lizenz: CC BY 4.0

http://phaidra.univie.ac.at/o:992840Lizenz: CC BY 4.0

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Verknüpfung zur Publikation in Scopus

Isoperimetrische Struktur von Anfangsdaten der Einstein-Gleichungen
Eichmair, M. (Projektleiter*in)
1/01/17 → 31/12/24
Projekt: Forschungsförderung

Zitationsweisen

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Characterization of Large Isoperimetric Regions in Asymptotically Hyperbolic Initial Data

Abstract

Fördermittel

ÖFOS 2012

Zugriff auf Dokument

Andere Dateien und Links

Fingerprint

Projekte

Isoperimetrische Struktur von Anfangsdaten der Einstein-Gleichungen

Zitationsweisen