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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1112.0878","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-05T10:33:21Z","cross_cats_sorted":[],"title_canon_sha256":"fbca0765a412673dd71ea60be3a565aeb72d7594254b21ec779ffb6d34cd1cef","abstract_canon_sha256":"ea147978414e43463cc27b12a73ea40d6796d22487472b160bdebdbbbd8342d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:59.677275Z","signature_b64":"azbgAWT2GERkD4mwLAowlk+JA2KSVJTIyZPhDRqiJila/47pAufjLA5ZjY6MzAPu9H1GJvleKp8dnSCXppYcBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49b8ee1211c23709182f9368680fa4b597bebe264a666ce93f3640c410291f37","last_reissued_at":"2026-05-18T00:47:59.676525Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:59.676525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1112.0878","created_at":"2026-05-18T00:47:59.676637+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.0878v2","created_at":"2026-05-18T00:47:59.676637+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0878","created_at":"2026-05-18T00:47:59.676637+00:00"},{"alias_kind":"pith_short_12","alias_value":"JG4O4EQRYI3Q","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"JG4O4EQRYI3QSGBP","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"JG4O4EQR","created_at":"2026-05-18T12:26:32.869790+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JG4O4EQRYI3QSGBPSNUGQD5EWW","json":"https://pith.science/pith/JG4O4EQRYI3QSGBPSNUGQD5EWW.json","graph_json":"https://pith.science/api/pith-number/JG4O4EQRYI3QSGBPSNUGQD5EWW/graph.json","events_json":"https://pith.science/api/pith-number/JG4O4EQRYI3QSGBPSNUGQD5EWW/events.json","paper":"https://pith.science/paper/JG4O4EQR"},"agent_actions":{"view_html":"https://pith.science/pith/JG4O4EQRYI3QSGBPSNUGQD5EWW","download_json":"https://pith.science/pith/JG4O4EQRYI3QSGBPSNUGQD5EWW.json","view_paper":"https://pith.science/paper/JG4O4EQR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.0878&json=true","fetch_graph":"https://pith.science/api/pith-number/JG4O4EQRYI3QSGBPSNUGQD5EWW/graph.json","fetch_events":"https://pith.science/api/pith-number/JG4O4EQRYI3QSGBPSNUGQD5EWW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JG4O4EQRYI3QSGBPSNUGQD5EWW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JG4O4EQRYI3QSGBPSNUGQD5EWW/action/storage_attestation","attest_author":"https://pith.science/pith/JG4O4EQRYI3QSGBPSNUGQD5EWW/action/author_attestation","sign_citation":"https://pith.science/pith/JG4O4EQRYI3QSGBPSNUGQD5EWW/action/citation_signature","submit_replication":"https://pith.science/pith/JG4O4EQRYI3QSGBPSNUGQD5EWW/action/replication_record"}},"created_at":"2026-05-18T00:47:59.676637+00:00","updated_at":"2026-05-18T00:47:59.676637+00:00"}