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We show that there exists a smooth closed embedded minimal hypersurface in $(M,g)$ of volume bounded by $C V^{\\frac{n-1}{n}}$, where $V$ is the total volume of $(M,g)$ and $C$ is a constant that depends only on $n$. When $Ric(M,g_0) \\geq -(n-1)$ we obtain a similar bound with constant $C$ depending only on $n$ and the volume of $(M,g_0)$.\n  Our second result concerns manifolds $(M,g)$ of positive Ricci curvatu"},"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":"1408.3656","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-15T21:29:28Z","cross_cats_sorted":[],"title_canon_sha256":"b5af7374ff4f79e0e4ee97e1441f589df74a7b7b1d6bc27d4e469811e9bbece2","abstract_canon_sha256":"069750b83ad97ba3f4f3c57a2551280070e06ef149771d15f4dcb1917915bdc2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:43.332096Z","signature_b64":"G/i/mgNkB+gF4cOBqXwxaw6VM7XtJl9zZVyIVCJhnx/PSbIC1R2Z0v3syx01Pw50xTP4Q6VENrdgFpZ3R2cYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d09aad3d484abe686e82dd06bfad85a918d19aefe3f95f3fd93d63559336535","last_reissued_at":"2026-05-18T01:30:43.331399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:43.331399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Width, Ricci curvature and minimal hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Parker Glynn-Adey, Yevgeny Liokumovich","submitted_at":"2014-08-15T21:29:28Z","abstract_excerpt":"Let $(M,g_0)$ be a closed Riemannian manifold of dimension $n$, for $3 \\leq n \\leq 7$, and non-negative Ricci curvature. 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When $Ric(M,g_0) \\geq -(n-1)$ we obtain a similar bound with constant $C$ depending only on $n$ and the volume of $(M,g_0)$.\n  Our second result concerns manifolds $(M,g)$ of positive Ricci curvatu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3656","kind":"arxiv","version":4},"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":"1408.3656","created_at":"2026-05-18T01:30:43.331513+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.3656v4","created_at":"2026-05-18T01:30:43.331513+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3656","created_at":"2026-05-18T01:30:43.331513+00:00"},{"alias_kind":"pith_short_12","alias_value":"FUE2VU6UQSV6","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"FUE2VU6UQSV6NBXI","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"FUE2VU6U","created_at":"2026-05-18T12:28:28.263976+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/FUE2VU6UQSV6NBXIFXIGX6WYLK","json":"https://pith.science/pith/FUE2VU6UQSV6NBXIFXIGX6WYLK.json","graph_json":"https://pith.science/api/pith-number/FUE2VU6UQSV6NBXIFXIGX6WYLK/graph.json","events_json":"https://pith.science/api/pith-number/FUE2VU6UQSV6NBXIFXIGX6WYLK/events.json","paper":"https://pith.science/paper/FUE2VU6U"},"agent_actions":{"view_html":"https://pith.science/pith/FUE2VU6UQSV6NBXIFXIGX6WYLK","download_json":"https://pith.science/pith/FUE2VU6UQSV6NBXIFXIGX6WYLK.json","view_paper":"https://pith.science/paper/FUE2VU6U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.3656&json=true","fetch_graph":"https://pith.science/api/pith-number/FUE2VU6UQSV6NBXIFXIGX6WYLK/graph.json","fetch_events":"https://pith.science/api/pith-number/FUE2VU6UQSV6NBXIFXIGX6WYLK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FUE2VU6UQSV6NBXIFXIGX6WYLK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FUE2VU6UQSV6NBXIFXIGX6WYLK/action/storage_attestation","attest_author":"https://pith.science/pith/FUE2VU6UQSV6NBXIFXIGX6WYLK/action/author_attestation","sign_citation":"https://pith.science/pith/FUE2VU6UQSV6NBXIFXIGX6WYLK/action/citation_signature","submit_replication":"https://pith.science/pith/FUE2VU6UQSV6NBXIFXIGX6WYLK/action/replication_record"}},"created_at":"2026-05-18T01:30:43.331513+00:00","updated_at":"2026-05-18T01:30:43.331513+00:00"}