{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:2KD5VN7XNWFX3KUEXH22SBZT6U","short_pith_number":"pith:2KD5VN7X","schema_version":"1.0","canonical_sha256":"d287dab7f76d8b7daa84b9f5a90733f5160ed2949100c287111edb43102432d4","source":{"kind":"arxiv","id":"1803.07787","version":1},"attestation_state":"computed","paper":{"title":"First eigenvalues of geometric operators under the Yamabe flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Pak Tung Ho","submitted_at":"2018-03-21T08:01:33Z","abstract_excerpt":"Suppose $(M,g_0)$ is a compact Riemannian manifold without boundary of dimension $n\\geq 3$. Using the Yamabe flow, we obtain estimate for the first nonzero eigenvalue of the Laplacian of $g_0$ with negative scalar curvature in terms of the Yamabe metric in its conformal class. On the other hand, we prove that the first eigenvalue of some geometric operators on a compact Riemannian manifold is nondecreasing along the unnormalized Yamabe flow under suitable curvature assumption. Similar results are obtained for manifolds with boundary and for CR manifold."},"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":"1803.07787","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-21T08:01:33Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"d53a1a60f3b839603b51137f4c798e9c52254731fa33ade4e1c48ab4590fbca7","abstract_canon_sha256":"9455c7df497087f1dd5d08d4909a8db83023610ad43ad2a93ee8582462c5e54f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:28.956518Z","signature_b64":"X0z40YrUYSMKwt+1VbFqM0osNk+iyvFWulpU7+P7Mc0nQlEHUH0GMjUbyi/HEJUmRtLcJKwtQ+WI9l4INND+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d287dab7f76d8b7daa84b9f5a90733f5160ed2949100c287111edb43102432d4","last_reissued_at":"2026-05-18T00:20:28.955918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:28.955918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"First eigenvalues of geometric operators under the Yamabe flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Pak Tung Ho","submitted_at":"2018-03-21T08:01:33Z","abstract_excerpt":"Suppose $(M,g_0)$ is a compact Riemannian manifold without boundary of dimension $n\\geq 3$. Using the Yamabe flow, we obtain estimate for the first nonzero eigenvalue of the Laplacian of $g_0$ with negative scalar curvature in terms of the Yamabe metric in its conformal class. On the other hand, we prove that the first eigenvalue of some geometric operators on a compact Riemannian manifold is nondecreasing along the unnormalized Yamabe flow under suitable curvature assumption. Similar results are obtained for manifolds with boundary and for CR manifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07787","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":""},"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":"1803.07787","created_at":"2026-05-18T00:20:28.956010+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.07787v1","created_at":"2026-05-18T00:20:28.956010+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07787","created_at":"2026-05-18T00:20:28.956010+00:00"},{"alias_kind":"pith_short_12","alias_value":"2KD5VN7XNWFX","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"2KD5VN7XNWFX3KUE","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"2KD5VN7X","created_at":"2026-05-18T12:32:02.567920+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/2KD5VN7XNWFX3KUEXH22SBZT6U","json":"https://pith.science/pith/2KD5VN7XNWFX3KUEXH22SBZT6U.json","graph_json":"https://pith.science/api/pith-number/2KD5VN7XNWFX3KUEXH22SBZT6U/graph.json","events_json":"https://pith.science/api/pith-number/2KD5VN7XNWFX3KUEXH22SBZT6U/events.json","paper":"https://pith.science/paper/2KD5VN7X"},"agent_actions":{"view_html":"https://pith.science/pith/2KD5VN7XNWFX3KUEXH22SBZT6U","download_json":"https://pith.science/pith/2KD5VN7XNWFX3KUEXH22SBZT6U.json","view_paper":"https://pith.science/paper/2KD5VN7X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.07787&json=true","fetch_graph":"https://pith.science/api/pith-number/2KD5VN7XNWFX3KUEXH22SBZT6U/graph.json","fetch_events":"https://pith.science/api/pith-number/2KD5VN7XNWFX3KUEXH22SBZT6U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2KD5VN7XNWFX3KUEXH22SBZT6U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2KD5VN7XNWFX3KUEXH22SBZT6U/action/storage_attestation","attest_author":"https://pith.science/pith/2KD5VN7XNWFX3KUEXH22SBZT6U/action/author_attestation","sign_citation":"https://pith.science/pith/2KD5VN7XNWFX3KUEXH22SBZT6U/action/citation_signature","submit_replication":"https://pith.science/pith/2KD5VN7XNWFX3KUEXH22SBZT6U/action/replication_record"}},"created_at":"2026-05-18T00:20:28.956010+00:00","updated_at":"2026-05-18T00:20:28.956010+00:00"}