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arXiv · 1606.04626

Isoperimetry, scalar curvature, and mass in asymptotically flat Riemannian $3$-manifolds

Otis Chodosh·Michael Eichmair·Yuguang Shi·Haobin Yu
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Abstract

Let $(M, g)$ be an asymptotically flat Riemannian $3$-manifold with non-negative scalar curvature and positive mass. We show that each leaf of the canonical foliation through stable constant mean curvature surfaces of the end of $(M, g)$ is uniquely isoperimetric for the volume it encloses.

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Otis Chodosh, Michael Eichmair, Yuguang Shi, Haobin Yu. 2016-06-15. Isoperimetry, scalar curvature, and mass in asymptotically flat Riemannian $3$-manifolds. https://doi.org/10.1002/cpa.21981

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