Characterization of large isoperimetric regions in asymptotically hyperbolic initial data
The main result is the following: Theorem. Let $(M,g)$ be a complete Riemannian 3-manifold with scalar curvature $R\ge-6$ that is asymptotic to Schwarzschild-anti-de Sitter with mass $m>0$. Let $\partial M$ be connected and the only $H=2$ surface in the manifold $(M,g)$. If there is $V_0>1$ and $\Omega\subset M$ is an isoperimetric region of Volume $V$ where $V\ge V_0$, then $\Omega$ is bounded by $\partial M$ and a leaf of the canonical foliation. In the case when the manifold $(M,g)$ is Schwarzschild-anti-de Sitter, a similar result was proved by \textit{J. Corvino} et al. [Pac. J. Math. 231, No. 1, 63--84 (2007; Zbl 1154.53048)].
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