{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:TE44VYYUY5FUWY7OIIC5TFMFKQ","short_pith_number":"pith:TE44VYYU","schema_version":"1.0","canonical_sha256":"9939cae314c74b4b63ee4205d99585543d81b2ad1f8366074b1a4d311988fb22","source":{"kind":"arxiv","id":"1509.08993","version":2},"attestation_state":"computed","paper":{"title":"The Cheeger Constant, Isoperimetric Problems, and Hyperbolic Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.SP"],"primary_cat":"math.DG","authors_text":"Brian Benson","submitted_at":"2015-09-30T02:06:45Z","abstract_excerpt":"We give a brief literature review of the isoperimetric problem and discuss its relationship with the Cheeger constant of Riemannian $n$-manifolds. For some non-compact, finite area 2-manifolds, we prove the existence and regularity of subsets whose isoperimetric ratio is equal to the Cheeger constant. To do this, we use results of Hass-Morgan for the isoperimetric problem of these manifolds. We also give an example of a finite area 2-manifold where no such subset exists. Using work of Adams-Morgan, we classify all such subsets of geometrically finite hyperbolic surfaces where such subsets alwa"},"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":"1509.08993","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-30T02:06:45Z","cross_cats_sorted":["math.GT","math.SP"],"title_canon_sha256":"afef278788f1160385d4ac89c83816e6a6bec034a0474cdd87514dc9beb766fc","abstract_canon_sha256":"495c8f5d9e1a11e257882b6a8f5e210c3ea148169d7c4cb33f0b40c04fdc0a86"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:18.571645Z","signature_b64":"H1BqVuJb3STsexlIHu8AswX5lM1LrZgIgUPd7R5G4UZaZcbJq9cwuxjBrux2F8ZWoDqqd3IuwADdtH0e0+bjAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9939cae314c74b4b63ee4205d99585543d81b2ad1f8366074b1a4d311988fb22","last_reissued_at":"2026-05-18T01:23:18.570880Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:18.570880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Cheeger Constant, Isoperimetric Problems, and Hyperbolic Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.SP"],"primary_cat":"math.DG","authors_text":"Brian Benson","submitted_at":"2015-09-30T02:06:45Z","abstract_excerpt":"We give a brief literature review of the isoperimetric problem and discuss its relationship with the Cheeger constant of Riemannian $n$-manifolds. For some non-compact, finite area 2-manifolds, we prove the existence and regularity of subsets whose isoperimetric ratio is equal to the Cheeger constant. To do this, we use results of Hass-Morgan for the isoperimetric problem of these manifolds. We also give an example of a finite area 2-manifold where no such subset exists. Using work of Adams-Morgan, we classify all such subsets of geometrically finite hyperbolic surfaces where such subsets alwa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08993","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":"1509.08993","created_at":"2026-05-18T01:23:18.571004+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.08993v2","created_at":"2026-05-18T01:23:18.571004+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08993","created_at":"2026-05-18T01:23:18.571004+00:00"},{"alias_kind":"pith_short_12","alias_value":"TE44VYYUY5FU","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"TE44VYYUY5FUWY7O","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"TE44VYYU","created_at":"2026-05-18T12:29:42.218222+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/TE44VYYUY5FUWY7OIIC5TFMFKQ","json":"https://pith.science/pith/TE44VYYUY5FUWY7OIIC5TFMFKQ.json","graph_json":"https://pith.science/api/pith-number/TE44VYYUY5FUWY7OIIC5TFMFKQ/graph.json","events_json":"https://pith.science/api/pith-number/TE44VYYUY5FUWY7OIIC5TFMFKQ/events.json","paper":"https://pith.science/paper/TE44VYYU"},"agent_actions":{"view_html":"https://pith.science/pith/TE44VYYUY5FUWY7OIIC5TFMFKQ","download_json":"https://pith.science/pith/TE44VYYUY5FUWY7OIIC5TFMFKQ.json","view_paper":"https://pith.science/paper/TE44VYYU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.08993&json=true","fetch_graph":"https://pith.science/api/pith-number/TE44VYYUY5FUWY7OIIC5TFMFKQ/graph.json","fetch_events":"https://pith.science/api/pith-number/TE44VYYUY5FUWY7OIIC5TFMFKQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TE44VYYUY5FUWY7OIIC5TFMFKQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TE44VYYUY5FUWY7OIIC5TFMFKQ/action/storage_attestation","attest_author":"https://pith.science/pith/TE44VYYUY5FUWY7OIIC5TFMFKQ/action/author_attestation","sign_citation":"https://pith.science/pith/TE44VYYUY5FUWY7OIIC5TFMFKQ/action/citation_signature","submit_replication":"https://pith.science/pith/TE44VYYUY5FUWY7OIIC5TFMFKQ/action/replication_record"}},"created_at":"2026-05-18T01:23:18.571004+00:00","updated_at":"2026-05-18T01:23:18.571004+00:00"}