{"paper":{"title":"Stable constant mean curvature surfaces with free boundary in slabs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Rabah Souam","submitted_at":"2018-02-19T21:01:32Z","abstract_excerpt":"We study stable constant mean curvature (CMC) hypersurfaces $\\Sigma$ in slabs in a product space $M\\times\\r,$ where $M$ is an orientable Riemannian manifold. We obtain a characterization of stable cylinders and prove that if $\\Sigma$ is not a cylinder then it is locally a vertical graph. Moreover, in case $M$ is $\\h^n,\\r^n$ or $\\s_+^n$ and each of its boundary components is embedded then $\\Sigma$ is rotationally invariant. When $M$ has dimension 2 and Gaussian curvature bounded from below by a positive constant $\\kappa,$ we prove there is no stable CMC with free boundary connecting the boundar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06848","kind":"arxiv","version":3},"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"}