Global uniqueness of large stable CMC spheres in asymptotically flat Riemannian 3-manifolds

Otis Chodosh; Michael Eichmair

doi:10.1215/00127094-2021-0043

15 January 2022 Global uniqueness of large stable CMC spheres in asymptotically flat Riemannian 3-manifolds

Otis Chodosh, Michael Eichmair

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Abstract

Let $(M,g)$ be a complete Riemannian 3-manifold that is asymptotic to Schwarzschild with positive mass and whose scalar curvature vanishes. We unconditionally characterize the large, embedded stable constant mean curvature (CMC) spheres in $(M,g)$ .

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Otis Chodosh. Michael Eichmair. "Global uniqueness of large stable CMC spheres in asymptotically flat Riemannian 3-manifolds." Duke Math. J. 171 (1) 1 - 31, 15 January 2022. https://doi.org/10.1215/00127094-2021-0043

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Received: 4 October 2019; Revised: 17 August 2020; Published: 15 January 2022

First available in Project Euclid: 17 January 2022

MathSciNet: MR4364730

zbMATH: 1491.53069

Digital Object Identifier: 10.1215/00127094-2021-0043

Subjects:

Primary: 53C20

Keywords: asymptotically flat , constant mean curvature , Hawking mass , Minkowski inequality , Scalar curvature , Schwarzschild

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