{"paper":{"title":"Halfspace type Theorems for Self-Shrinkers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jose M. Espinar, Marcos P. Cavalcante","submitted_at":"2014-12-11T18:38:32Z","abstract_excerpt":"In this short paper we extend the classical Hoffman-Meeks Halfspace Theorem to self-shrinkers, that is: \"Let $P $ be a hyperplane passing through the origin. The only properly immersed self-shrinker $\\Sigma$ contained in one of the closed half-space determined by $P$ is $\\Sigma = P$.\"\n  Our proof is geometric and uses a catenoid type hypersurface discovered by Kleene-Moller. Also, using a similar geometric idea, we obtain that the only complete self-shrinker properly immersed in an closed cylinder $ \\overline{B ^{k+1} (R)} \\times \\mathbb{R}^{n-k}\\subset \\mathbb R^{n+1}$, for some $k\\in \\{1, \\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3754","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"}