{"paper":{"title":"Complete negatively curved immersed ends in $\\Bbb R^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"S\\'ergio Mendon\\c{c}a","submitted_at":"2014-05-06T14:24:00Z","abstract_excerpt":"This paper extends, in a sharp way, the famous Efimov's Theorem to immersed ends in $\\real^3$. More precisely, let $M$ be a non-compact connected surface with compact boundary. Then there is no complete isometric immersion of $M$ into $\\Bbb R^3$ satisfying that $\\int_M |K|=+\\infty$ and $K\\le-\\kappa<0$, where $\\kappa$ is a positive constant and $K$ is the Gaussian curvature of $M$. In particular Efimov's Theorem holds for complete Hadamard immersed surfaces, whose Gaussian curvature $K$ is bounded away from zero outside a compact set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1280","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"}