{"paper":{"title":"Mean curvature in manifolds with Ricci curvature bounded from below","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ailana Fraser, Jaigyoung Choe","submitted_at":"2016-05-21T07:34:31Z","abstract_excerpt":"Let $M$ be a compact Riemannian manifold of nonnegative Ricci curvature and $\\Sigma$ a compact embedded 2-sided minimal hypersurface in $M$. It is proved that there is a dichotomy: If $\\Sigma$ does not separate $M$ then $\\Sigma$ is totally geodesic and $M\\setminus\\Sigma$ is isometric to the Riemannian product $\\Sigma\\times(a,b)$, and if $\\Sigma$ separates $M$ then the map $i_*:\\pi_1(\\Sigma)\\rightarrow \\pi_1(M)$ induced by inclusion is surjective. This surjectivity is also proved for a compact 2-sided hypersurface with mean curvature $H\\geq(n-1)\\sqrt{k}$ in a manifold of Ricci curvature $Ric_M\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06602","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"}