{"paper":{"title":"On the structure of complete 3-manifolds with nonnegative scalar curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jose M. Espinar","submitted_at":"2011-12-05T10:33:21Z","abstract_excerpt":"In this paper we will show the following result: Let $\\mathcal{N} $ be a complete (noncompact) connected orientable Riemannian three-manifold with nonnegative scalar curvature $S \\geq 0$ and bounded sectional curvature $ K_{s} \\leq K $. Suposse that $\\Sigma \\subset \\mathcal{N} $ is a complete orientable connected area-minimizing cylinder so that $\\pi_1 (\\Sigma) \\in \\pi_1 (\\mathcal{N})$. Then $\\mathcal{N}$ is locally isometric either to $\\mathbb{S} ^1 \\times \\mathbb{R} ^2 $ or $\\mathbb{S}^1 \\times \\mathbb{S}^1 \\times \\mathbb{R}$ (with the standard product metric).\n  As a corollary, we will obta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0878","kind":"arxiv","version":2},"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"}