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, Michael Eichmair, Yuguang Shi, Jintian Zhu

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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 language	English (US)
Pages (from-to)	777-798
Number of pages	22
Journal	Communications In Mathematical Physics
Volume	368
Issue number	2
DOIs	https://doi.org/10.1007/s00220-019-03354-2
State	Published - Jun 1 2019

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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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.",

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AU - Chodosh, Otis

AU - Eichmair, Michael

AU - Shi, Yuguang

AU - Zhu, Jintian

PY - 2019/6/1

Y1 - 2019/6/1

N2 - 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.

AB - 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.

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JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 2

ER -

Characterization of Large Isoperimetric Regions in Asymptotically Hyperbolic Initial Data

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