{"paper":{"title":"Stable capillary hypersurfaces in a half-space or a slab","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Abdelhamid Ainouz, Rabah Souam","submitted_at":"2014-11-16T10:47:31Z","abstract_excerpt":"We study stable immersed capillary hypersurfaces in a domain $\\mathcal B$ which is either a half-space or a slab in the Euclidean space $\\Bbb R^{n+1}.$ We prove that such a hypersurface $\\Sigma$ is rotationally symmetric in the following cases:\n  (1) $n=2$, $\\mathcal B$ is a slab and $\\Sigma$ has genus zero,\n  (2) $n\\geq 2$, $\\mathcal B$ is a slab, the angle of contact is $\\pi/2$ and each component of $\\partial\\Sigma$ is embedded,\n  (3) $n\\geq 2,$ $\\mathcal B$ is a half-space, the angle of contact is $<\\pi/2$ and each component of $\\partial\\Sigma$ is embedded.\n  Moreover, in case (2), if not a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4241","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"}