{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2KD5VN7XNWFX3KUEXH22SBZT6U","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9455c7df497087f1dd5d08d4909a8db83023610ad43ad2a93ee8582462c5e54f","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-21T08:01:33Z","title_canon_sha256":"d53a1a60f3b839603b51137f4c798e9c52254731fa33ade4e1c48ab4590fbca7"},"schema_version":"1.0","source":{"id":"1803.07787","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07787","created_at":"2026-05-18T00:20:28Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07787v1","created_at":"2026-05-18T00:20:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07787","created_at":"2026-05-18T00:20:28Z"},{"alias_kind":"pith_short_12","alias_value":"2KD5VN7XNWFX","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2KD5VN7XNWFX3KUE","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2KD5VN7X","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:1181eace74334c6cd6f8b58e2edd429d10162c18b6e51e74cf0e5a2222822626","target":"graph","created_at":"2026-05-18T00:20:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Pak Tung Ho","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-21T08:01:33Z","title":"First eigenvalues of geometric operators under the Yamabe flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07787","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:28c8f21d507ce32828472902c2952df68f523aefd848477ac0bbca6ce68bec7b","target":"record","created_at":"2026-05-18T00:20:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9455c7df497087f1dd5d08d4909a8db83023610ad43ad2a93ee8582462c5e54f","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-21T08:01:33Z","title_canon_sha256":"d53a1a60f3b839603b51137f4c798e9c52254731fa33ade4e1c48ab4590fbca7"},"schema_version":"1.0","source":{"id":"1803.07787","kind":"arxiv","version":1}},"canonical_sha256":"d287dab7f76d8b7daa84b9f5a90733f5160ed2949100c287111edb43102432d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d287dab7f76d8b7daa84b9f5a90733f5160ed2949100c287111edb43102432d4","first_computed_at":"2026-05-18T00:20:28.955918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:28.955918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X0z40YrUYSMKwt+1VbFqM0osNk+iyvFWulpU7+P7Mc0nQlEHUH0GMjUbyi/HEJUmRtLcJKwtQ+WI9l4INND+Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:28.956518Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.07787","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28c8f21d507ce32828472902c2952df68f523aefd848477ac0bbca6ce68bec7b","sha256:1181eace74334c6cd6f8b58e2edd429d10162c18b6e51e74cf0e5a2222822626"],"state_sha256":"9d555028e7a2980caf2a2ed839f93d760be37f4d982954f8672a40d07634b690"}