{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:XRDRBY5B3Z2N6J5D3HKFW5IVVQ","short_pith_number":"pith:XRDRBY5B","schema_version":"1.0","canonical_sha256":"bc4710e3a1de74df27a3d9d45b7515ac38fed2b85553c88d8797e74edfb8c396","source":{"kind":"arxiv","id":"1806.11441","version":2},"attestation_state":"computed","paper":{"title":"A nonexistence theorem for proper biharmonic maps into general Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Volker Branding, Yong Luo","submitted_at":"2018-06-28T08:09:24Z","abstract_excerpt":"In this note we prove a nonexistence result for proper biharmonic maps from complete non-compact Riemannian manifolds of dimension \\(m=\\dim M\\geq 3\\) with infinite volume that admit an Euclidean type Sobolev inequality into general Riemannian manifolds by assuming finiteness of $\\|\\tau(\\phi)\\|_{L^p(M)}, p>1$ and smallness of $\\|d\\phi\\|_{L^m(M)}$. This is an improvement of a recent result of the first named author, where he assumed $2<p<m$. As applications we also get several nonexistence results for proper biharmonic submersions from complete non-compact manifolds into general Riemannian manif"},"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":"1806.11441","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-28T08:09:24Z","cross_cats_sorted":[],"title_canon_sha256":"a42e85b2c6dcfe67eec3b51b64e4524e8a458ade9545584ccf4eda12a76c41eb","abstract_canon_sha256":"42f5b2818def2ebef842635e5800aded0e341eee1c835dd9bfe20d9d55587985"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:48.725348Z","signature_b64":"49B2NDDDmJYuSpoI30/W0SbT8eiLmubXw8qUhs6tVeZGrco7U5G0JP8Vvcp5VZUmATEdYEzn3JklH/8aYGL+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc4710e3a1de74df27a3d9d45b7515ac38fed2b85553c88d8797e74edfb8c396","last_reissued_at":"2026-05-18T00:10:48.724779Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:48.724779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A nonexistence theorem for proper biharmonic maps into general Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Volker Branding, Yong Luo","submitted_at":"2018-06-28T08:09:24Z","abstract_excerpt":"In this note we prove a nonexistence result for proper biharmonic maps from complete non-compact Riemannian manifolds of dimension \\(m=\\dim M\\geq 3\\) with infinite volume that admit an Euclidean type Sobolev inequality into general Riemannian manifolds by assuming finiteness of $\\|\\tau(\\phi)\\|_{L^p(M)}, p>1$ and smallness of $\\|d\\phi\\|_{L^m(M)}$. This is an improvement of a recent result of the first named author, where he assumed $2<p<m$. As applications we also get several nonexistence results for proper biharmonic submersions from complete non-compact manifolds into general Riemannian manif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.11441","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":"1806.11441","created_at":"2026-05-18T00:10:48.724856+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.11441v2","created_at":"2026-05-18T00:10:48.724856+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.11441","created_at":"2026-05-18T00:10:48.724856+00:00"},{"alias_kind":"pith_short_12","alias_value":"XRDRBY5B3Z2N","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"XRDRBY5B3Z2N6J5D","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"XRDRBY5B","created_at":"2026-05-18T12:33:01.666342+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/XRDRBY5B3Z2N6J5D3HKFW5IVVQ","json":"https://pith.science/pith/XRDRBY5B3Z2N6J5D3HKFW5IVVQ.json","graph_json":"https://pith.science/api/pith-number/XRDRBY5B3Z2N6J5D3HKFW5IVVQ/graph.json","events_json":"https://pith.science/api/pith-number/XRDRBY5B3Z2N6J5D3HKFW5IVVQ/events.json","paper":"https://pith.science/paper/XRDRBY5B"},"agent_actions":{"view_html":"https://pith.science/pith/XRDRBY5B3Z2N6J5D3HKFW5IVVQ","download_json":"https://pith.science/pith/XRDRBY5B3Z2N6J5D3HKFW5IVVQ.json","view_paper":"https://pith.science/paper/XRDRBY5B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.11441&json=true","fetch_graph":"https://pith.science/api/pith-number/XRDRBY5B3Z2N6J5D3HKFW5IVVQ/graph.json","fetch_events":"https://pith.science/api/pith-number/XRDRBY5B3Z2N6J5D3HKFW5IVVQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XRDRBY5B3Z2N6J5D3HKFW5IVVQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XRDRBY5B3Z2N6J5D3HKFW5IVVQ/action/storage_attestation","attest_author":"https://pith.science/pith/XRDRBY5B3Z2N6J5D3HKFW5IVVQ/action/author_attestation","sign_citation":"https://pith.science/pith/XRDRBY5B3Z2N6J5D3HKFW5IVVQ/action/citation_signature","submit_replication":"https://pith.science/pith/XRDRBY5B3Z2N6J5D3HKFW5IVVQ/action/replication_record"}},"created_at":"2026-05-18T00:10:48.724856+00:00","updated_at":"2026-05-18T00:10:48.724856+00:00"}