{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:G7Z4HUPCGGRJZRM5OEQ5N6WEGO","short_pith_number":"pith:G7Z4HUPC","schema_version":"1.0","canonical_sha256":"37f3c3d1e231a29cc59d7121d6fac4339ff8178af68245bc8d79cad7dbfae5d2","source":{"kind":"arxiv","id":"1011.6583","version":3},"attestation_state":"computed","paper":{"title":"Non existence of constant mean curvature graphs on circular annuli of $\\mathbb{H}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Cosimo Senni","submitted_at":"2010-11-30T15:40:24Z","abstract_excerpt":"We show a non existence result for solutions of the prescribed mean curvature equation in the product manifold $\\mathbb{H}^2 \\times \\R$, where $\\mathbb{H}^2$ is the real hyperbolic plane. More precisely we prove a-priori estimates for graphs with constant mean curvature $h \\in (0, 1/2]$ on circular annuli of $\\mathbb{H}^2$. For $0 < h < 1/2$ we obtain an estimate from above on any circular annulus and one from below on annuli with a small hole, the size of the hole depending on $h$. For $h = 1/2$ we obtain both estimates for any circular annulus. All the estimates depend only on the thickness "},"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":"1011.6583","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-11-30T15:40:24Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"399010c22db5734b79ce5a2cf4fd96f4862da9e9676d2cbf796861cc296d2ba9","abstract_canon_sha256":"839668d0240d47d92cf572b51452e690d73221d5117abe30e3ba388150b4234a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:38.931217Z","signature_b64":"Z/fARwVfuxqKDuSqm0lYWY4jNszEOuuMn/21lq273rzZev3a/b9afimcBcJW7DGH++WRW6f8D5h5jvPcU7rtCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37f3c3d1e231a29cc59d7121d6fac4339ff8178af68245bc8d79cad7dbfae5d2","last_reissued_at":"2026-05-18T04:25:38.930789Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:38.930789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non existence of constant mean curvature graphs on circular annuli of $\\mathbb{H}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Cosimo Senni","submitted_at":"2010-11-30T15:40:24Z","abstract_excerpt":"We show a non existence result for solutions of the prescribed mean curvature equation in the product manifold $\\mathbb{H}^2 \\times \\R$, where $\\mathbb{H}^2$ is the real hyperbolic plane. More precisely we prove a-priori estimates for graphs with constant mean curvature $h \\in (0, 1/2]$ on circular annuli of $\\mathbb{H}^2$. For $0 < h < 1/2$ we obtain an estimate from above on any circular annulus and one from below on annuli with a small hole, the size of the hole depending on $h$. For $h = 1/2$ we obtain both estimates for any circular annulus. All the estimates depend only on the thickness "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6583","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1011.6583","created_at":"2026-05-18T04:25:38.930856+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.6583v3","created_at":"2026-05-18T04:25:38.930856+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.6583","created_at":"2026-05-18T04:25:38.930856+00:00"},{"alias_kind":"pith_short_12","alias_value":"G7Z4HUPCGGRJ","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"G7Z4HUPCGGRJZRM5","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"G7Z4HUPC","created_at":"2026-05-18T12:26:07.630475+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/G7Z4HUPCGGRJZRM5OEQ5N6WEGO","json":"https://pith.science/pith/G7Z4HUPCGGRJZRM5OEQ5N6WEGO.json","graph_json":"https://pith.science/api/pith-number/G7Z4HUPCGGRJZRM5OEQ5N6WEGO/graph.json","events_json":"https://pith.science/api/pith-number/G7Z4HUPCGGRJZRM5OEQ5N6WEGO/events.json","paper":"https://pith.science/paper/G7Z4HUPC"},"agent_actions":{"view_html":"https://pith.science/pith/G7Z4HUPCGGRJZRM5OEQ5N6WEGO","download_json":"https://pith.science/pith/G7Z4HUPCGGRJZRM5OEQ5N6WEGO.json","view_paper":"https://pith.science/paper/G7Z4HUPC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.6583&json=true","fetch_graph":"https://pith.science/api/pith-number/G7Z4HUPCGGRJZRM5OEQ5N6WEGO/graph.json","fetch_events":"https://pith.science/api/pith-number/G7Z4HUPCGGRJZRM5OEQ5N6WEGO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G7Z4HUPCGGRJZRM5OEQ5N6WEGO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G7Z4HUPCGGRJZRM5OEQ5N6WEGO/action/storage_attestation","attest_author":"https://pith.science/pith/G7Z4HUPCGGRJZRM5OEQ5N6WEGO/action/author_attestation","sign_citation":"https://pith.science/pith/G7Z4HUPCGGRJZRM5OEQ5N6WEGO/action/citation_signature","submit_replication":"https://pith.science/pith/G7Z4HUPCGGRJZRM5OEQ5N6WEGO/action/replication_record"}},"created_at":"2026-05-18T04:25:38.930856+00:00","updated_at":"2026-05-18T04:25:38.930856+00:00"}