{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:RKSXFYOGDP5F23NRPYPNHUTBUH","short_pith_number":"pith:RKSXFYOG","schema_version":"1.0","canonical_sha256":"8aa572e1c61bfa5d6db17e1ed3d261a1f4fbb34bad8f069a37542628811b94e8","source":{"kind":"arxiv","id":"2408.07823","version":1},"attestation_state":"computed","paper":{"title":"Nonexistence of minimizers for the second conformal eigenvalue near the round sphere in low dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Bruno Premoselli, J\\'er\\^ome V\\'etois","submitted_at":"2024-08-14T21:33:10Z","abstract_excerpt":"We consider the problem of minimizing the second conformal eigenvalue of the conformal Laplacian in a conformal class of metrics with renormalized volume. We prove, in dimensions $n\\in\\left\\{3,\\dotsc,10\\right\\}$, that a minimizer for this problem does not exist for metrics sufficiently close to the round metric on the sphere. This is in striking contrast with the situation in dimensions $n \\ge 11$, where Ammann and Humbert obtained the existence of minimizers for the second conformal eigenvalue on any smooth closed non-locally conformally flat manifold. As a byproduct of our techniques, we als"},"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":"2408.07823","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2024-08-14T21:33:10Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"ea109f043e0f8faa5231e75f476a38abb7bdf99eb8b02eb5310c302a06c8ff61","abstract_canon_sha256":"ac9db201b8c7c7f619094f9ee85730a42d34f7c2abb3168c12862fefd7aef27a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:55:40.381775Z","signature_b64":"5sUqI8/b7IGqDrQ56w8AjYQpO/fFVL0bNmehILP2AtC0acHVCRQmDfJxxRQEjMokbLLVWlzJjs4QKyCqjhztDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8aa572e1c61bfa5d6db17e1ed3d261a1f4fbb34bad8f069a37542628811b94e8","last_reissued_at":"2026-07-05T08:55:40.381305Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:55:40.381305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonexistence of minimizers for the second conformal eigenvalue near the round sphere in low dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Bruno Premoselli, J\\'er\\^ome V\\'etois","submitted_at":"2024-08-14T21:33:10Z","abstract_excerpt":"We consider the problem of minimizing the second conformal eigenvalue of the conformal Laplacian in a conformal class of metrics with renormalized volume. We prove, in dimensions $n\\in\\left\\{3,\\dotsc,10\\right\\}$, that a minimizer for this problem does not exist for metrics sufficiently close to the round metric on the sphere. This is in striking contrast with the situation in dimensions $n \\ge 11$, where Ammann and Humbert obtained the existence of minimizers for the second conformal eigenvalue on any smooth closed non-locally conformally flat manifold. As a byproduct of our techniques, we als"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.07823","kind":"arxiv","version":1},"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/2408.07823/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":"2408.07823","created_at":"2026-07-05T08:55:40.381375+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.07823v1","created_at":"2026-07-05T08:55:40.381375+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.07823","created_at":"2026-07-05T08:55:40.381375+00:00"},{"alias_kind":"pith_short_12","alias_value":"RKSXFYOGDP5F","created_at":"2026-07-05T08:55:40.381375+00:00"},{"alias_kind":"pith_short_16","alias_value":"RKSXFYOGDP5F23NR","created_at":"2026-07-05T08:55:40.381375+00:00"},{"alias_kind":"pith_short_8","alias_value":"RKSXFYOG","created_at":"2026-07-05T08:55:40.381375+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.31869","citing_title":"Eigenvalue optimization via a first-variation formula","ref_index":31,"is_internal_anchor":false},{"citing_arxiv_id":"2511.10553","citing_title":"Sign-changing solutions to the Yamabe problem on manifolds with boundary","ref_index":34,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RKSXFYOGDP5F23NRPYPNHUTBUH","json":"https://pith.science/pith/RKSXFYOGDP5F23NRPYPNHUTBUH.json","graph_json":"https://pith.science/api/pith-number/RKSXFYOGDP5F23NRPYPNHUTBUH/graph.json","events_json":"https://pith.science/api/pith-number/RKSXFYOGDP5F23NRPYPNHUTBUH/events.json","paper":"https://pith.science/paper/RKSXFYOG"},"agent_actions":{"view_html":"https://pith.science/pith/RKSXFYOGDP5F23NRPYPNHUTBUH","download_json":"https://pith.science/pith/RKSXFYOGDP5F23NRPYPNHUTBUH.json","view_paper":"https://pith.science/paper/RKSXFYOG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.07823&json=true","fetch_graph":"https://pith.science/api/pith-number/RKSXFYOGDP5F23NRPYPNHUTBUH/graph.json","fetch_events":"https://pith.science/api/pith-number/RKSXFYOGDP5F23NRPYPNHUTBUH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RKSXFYOGDP5F23NRPYPNHUTBUH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RKSXFYOGDP5F23NRPYPNHUTBUH/action/storage_attestation","attest_author":"https://pith.science/pith/RKSXFYOGDP5F23NRPYPNHUTBUH/action/author_attestation","sign_citation":"https://pith.science/pith/RKSXFYOGDP5F23NRPYPNHUTBUH/action/citation_signature","submit_replication":"https://pith.science/pith/RKSXFYOGDP5F23NRPYPNHUTBUH/action/replication_record"}},"created_at":"2026-07-05T08:55:40.381375+00:00","updated_at":"2026-07-05T08:55:40.381375+00:00"}