Characterization of large isoperimetric regions in asymptotically hyperbolic initial data

Abstract

Let $(M,g)$ be a complete Riemannian $3$-manifold asymptotic to Schwarzschild-anti-deSitter and with scalar curvature $R\ge -6$. 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 $R\ge -6$ 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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