{"paper":{"title":"Properly immersed surfaces in hyperbolic 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"\\'Alvaro K. Ramos, William H. Meeks III","submitted_at":"2016-03-07T15:39:51Z","abstract_excerpt":"We study complete finite topology immersed surfaces $\\Sigma$ in complete Riemannian $3$-manifolds $N$ with sectional curvature $K_N\\leq -a^2\\leq 0$, such that the absolute mean curvature function of $\\Sigma$ is bounded from above by $a$ and its injectivity radius function is not bounded away from zero on each of its annular end representatives. We prove that such a surface $\\Sigma$ must be proper in $N$ and its total curvature must be equal to $2\\pi \\chi(\\Sigma)$. If $N$ is a hyperbolic $3$-manifold of finite volume and $\\Sigma$ is a properly immersed surface of finite topology with nonnegativ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02116","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"}