{"paper":{"title":"On stable CMC hypersurfaces with free-boundary in a Euclidean Ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ezequiel Barbosa","submitted_at":"2016-06-30T20:47:18Z","abstract_excerpt":"In this note, we observe that if $B$ is a ball in a Euclidean space with dimension $n$, $n\\geq3$, then a stable CMC hypersurface $\\Sigma$ with free boundary in $B$ satisfies \\[ nA\\leq L\\leq nA\\left( \\frac{1+\\sqrt{1+4(n+1)H^2}}{2} \\right)\\,, \\] where $L$, $A$ and $H$ denote the length of $\\partial \\Sigma$, the area of $\\Sigma$ and the mean curvature of $\\Sigma$, respectively. Consequently, if the boundary $\\partial \\Sigma$ is embedded then $\\Sigma$ must be totally geodesic or starshaped with respect to the center of the ball. This result is an improvement of a theorem proved by A. Ros and E. Ve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00038","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"}