{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:7DMQWGQVH4DSDPWBI7755UX7KS","short_pith_number":"pith:7DMQWGQV","schema_version":"1.0","canonical_sha256":"f8d90b1a153f0721bec147ffded2ff54b2337e1e018d5ba7e5978bb681f37ba2","source":{"kind":"arxiv","id":"2405.02939","version":2},"attestation_state":"computed","paper":{"title":"Pogorelov type estimates for $(n-1)$-Hessian equations and related rigidity theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qiang Tu","submitted_at":"2024-05-05T14:00:27Z","abstract_excerpt":"In this paper, we establish Pogorelov type $C^2$ estimates for admissible solutions to the Dirichlet problem of $(n-1)$-Hessian equation based on a concavity inequality, which is inspired by the Lu-Tsai's work on the global curvature estimates for the $n-1$ curvature equation. As an application, we apply such estimates to obtain a rigidity theorems for admissible solutions of $(n-1)$-Hessian equation only under quadratic growth conditions. This result gives a positive answer to a open problem for $k$-Hessian equation, which is proposed by Chang-Yuan, in case $k=n-1$."},"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":"2405.02939","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-05-05T14:00:27Z","cross_cats_sorted":[],"title_canon_sha256":"8f935ceb0161f6e384660ecf0135546364da460381f704bb5b5c7901d06b8288","abstract_canon_sha256":"4f04f05ad91b43f2be96ac40c155782412666c6ca163496f4374582a868a83d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:55:09.270182Z","signature_b64":"ii3l4ReCxEeFx2edaUuAtO3SpnFqLcoWmzwfErJjt1pZL81VWFIUreU5FNenmIha1lktxTPNR7uObAsdQO/0AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8d90b1a153f0721bec147ffded2ff54b2337e1e018d5ba7e5978bb681f37ba2","last_reissued_at":"2026-07-05T09:55:09.269702Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:55:09.269702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pogorelov type estimates for $(n-1)$-Hessian equations and related rigidity theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qiang Tu","submitted_at":"2024-05-05T14:00:27Z","abstract_excerpt":"In this paper, we establish Pogorelov type $C^2$ estimates for admissible solutions to the Dirichlet problem of $(n-1)$-Hessian equation based on a concavity inequality, which is inspired by the Lu-Tsai's work on the global curvature estimates for the $n-1$ curvature equation. As an application, we apply such estimates to obtain a rigidity theorems for admissible solutions of $(n-1)$-Hessian equation only under quadratic growth conditions. This result gives a positive answer to a open problem for $k$-Hessian equation, which is proposed by Chang-Yuan, in case $k=n-1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.02939","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.02939/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2405.02939","created_at":"2026-07-05T09:55:09.269759+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.02939v2","created_at":"2026-07-05T09:55:09.269759+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.02939","created_at":"2026-07-05T09:55:09.269759+00:00"},{"alias_kind":"pith_short_12","alias_value":"7DMQWGQVH4DS","created_at":"2026-07-05T09:55:09.269759+00:00"},{"alias_kind":"pith_short_16","alias_value":"7DMQWGQVH4DSDPWB","created_at":"2026-07-05T09:55:09.269759+00:00"},{"alias_kind":"pith_short_8","alias_value":"7DMQWGQV","created_at":"2026-07-05T09:55:09.269759+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.11822","citing_title":"The Pogorelov estimates for the sum Hessian equation with rigidity theorem and parabolic versions","ref_index":43,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7DMQWGQVH4DSDPWBI7755UX7KS","json":"https://pith.science/pith/7DMQWGQVH4DSDPWBI7755UX7KS.json","graph_json":"https://pith.science/api/pith-number/7DMQWGQVH4DSDPWBI7755UX7KS/graph.json","events_json":"https://pith.science/api/pith-number/7DMQWGQVH4DSDPWBI7755UX7KS/events.json","paper":"https://pith.science/paper/7DMQWGQV"},"agent_actions":{"view_html":"https://pith.science/pith/7DMQWGQVH4DSDPWBI7755UX7KS","download_json":"https://pith.science/pith/7DMQWGQVH4DSDPWBI7755UX7KS.json","view_paper":"https://pith.science/paper/7DMQWGQV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.02939&json=true","fetch_graph":"https://pith.science/api/pith-number/7DMQWGQVH4DSDPWBI7755UX7KS/graph.json","fetch_events":"https://pith.science/api/pith-number/7DMQWGQVH4DSDPWBI7755UX7KS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7DMQWGQVH4DSDPWBI7755UX7KS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7DMQWGQVH4DSDPWBI7755UX7KS/action/storage_attestation","attest_author":"https://pith.science/pith/7DMQWGQVH4DSDPWBI7755UX7KS/action/author_attestation","sign_citation":"https://pith.science/pith/7DMQWGQVH4DSDPWBI7755UX7KS/action/citation_signature","submit_replication":"https://pith.science/pith/7DMQWGQVH4DSDPWBI7755UX7KS/action/replication_record"}},"created_at":"2026-07-05T09:55:09.269759+00:00","updated_at":"2026-07-05T09:55:09.269759+00:00"}