{"paper":{"title":"Characterization of large isoperimetric regions in asymptotically hyperbolic initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jintian Zhu, Michael Eichmair, Otis Chodosh, Yuguang Shi","submitted_at":"2018-04-02T11:05:22Z","abstract_excerpt":"Let $(M,g)$ be a complete Riemannian $3$-manifold asymptotic to Schwarzschild-anti-deSitter and with scalar curvature $R \\geq - 6$. 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 $R \\geq -6$ is necessary.\n  This is the first characterization result for large isoperimetric regions in the asymptotically hyperbolic setting that does not assume exact rotational symmetry at infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00447","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}