{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:4UTGWXETVTPFUQWA4CZIOPRQ7W","short_pith_number":"pith:4UTGWXET","schema_version":"1.0","canonical_sha256":"e5266b5c93acde5a42c0e0b2873e30fdb3557c9e8fa41da1c9f5ed6fb275d24b","source":{"kind":"arxiv","id":"1710.05537","version":3},"attestation_state":"computed","paper":{"title":"Hamiltonian stability for weighted measure and generalized Lagrangian mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Keita Kunikawa, Toru Kajigaya","submitted_at":"2017-10-16T07:00:23Z","abstract_excerpt":"In this paper, we generalize several results for the Hamiltonian stability and the mean curvature flow of Lagrangian submanifolds in a K\\\"ahler-Einstein manifold to more general K\\\"ahler manifolds including a Fano manifold equipped with a K\\\"ahler form $\\omega\\in 2\\pi c_1(M)$ by using the methodology proposed by T. Behrndt. Namely, we first consider a weighted measure on a Lagrangian submanifold $L$ in a K\\\"ahler manifold $M$ and investigate the variational problem of $L$ for the weighted volume functional. We call a stationary point of the weighted volume functional $f$-minimal, and define th"},"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":"1710.05537","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-16T07:00:23Z","cross_cats_sorted":[],"title_canon_sha256":"2bfc028198aac7f879a94f87b3845f3b874ae1b4c79785882b5586c3e756a5b3","abstract_canon_sha256":"e64bbdc6ba1d9ada11dc947b1a1b877901640708d02a97500235f5b5892d16e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:26.196843Z","signature_b64":"Ek4Xe0SGLDDBgiQggqSj0OdHCc5trIRLWvT2w94OjcWfNCb/wo1itWEkzHMky9zYTdh4NY4ia/i+zPNLvpSHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5266b5c93acde5a42c0e0b2873e30fdb3557c9e8fa41da1c9f5ed6fb275d24b","last_reissued_at":"2026-05-18T00:19:26.196251Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:26.196251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hamiltonian stability for weighted measure and generalized Lagrangian mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Keita Kunikawa, Toru Kajigaya","submitted_at":"2017-10-16T07:00:23Z","abstract_excerpt":"In this paper, we generalize several results for the Hamiltonian stability and the mean curvature flow of Lagrangian submanifolds in a K\\\"ahler-Einstein manifold to more general K\\\"ahler manifolds including a Fano manifold equipped with a K\\\"ahler form $\\omega\\in 2\\pi c_1(M)$ by using the methodology proposed by T. Behrndt. Namely, we first consider a weighted measure on a Lagrangian submanifold $L$ in a K\\\"ahler manifold $M$ and investigate the variational problem of $L$ for the weighted volume functional. We call a stationary point of the weighted volume functional $f$-minimal, and define th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05537","kind":"arxiv","version":3},"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":"1710.05537","created_at":"2026-05-18T00:19:26.196346+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.05537v3","created_at":"2026-05-18T00:19:26.196346+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05537","created_at":"2026-05-18T00:19:26.196346+00:00"},{"alias_kind":"pith_short_12","alias_value":"4UTGWXETVTPF","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"4UTGWXETVTPFUQWA","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"4UTGWXET","created_at":"2026-05-18T12:31:00.734936+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/4UTGWXETVTPFUQWA4CZIOPRQ7W","json":"https://pith.science/pith/4UTGWXETVTPFUQWA4CZIOPRQ7W.json","graph_json":"https://pith.science/api/pith-number/4UTGWXETVTPFUQWA4CZIOPRQ7W/graph.json","events_json":"https://pith.science/api/pith-number/4UTGWXETVTPFUQWA4CZIOPRQ7W/events.json","paper":"https://pith.science/paper/4UTGWXET"},"agent_actions":{"view_html":"https://pith.science/pith/4UTGWXETVTPFUQWA4CZIOPRQ7W","download_json":"https://pith.science/pith/4UTGWXETVTPFUQWA4CZIOPRQ7W.json","view_paper":"https://pith.science/paper/4UTGWXET","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.05537&json=true","fetch_graph":"https://pith.science/api/pith-number/4UTGWXETVTPFUQWA4CZIOPRQ7W/graph.json","fetch_events":"https://pith.science/api/pith-number/4UTGWXETVTPFUQWA4CZIOPRQ7W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4UTGWXETVTPFUQWA4CZIOPRQ7W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4UTGWXETVTPFUQWA4CZIOPRQ7W/action/storage_attestation","attest_author":"https://pith.science/pith/4UTGWXETVTPFUQWA4CZIOPRQ7W/action/author_attestation","sign_citation":"https://pith.science/pith/4UTGWXETVTPFUQWA4CZIOPRQ7W/action/citation_signature","submit_replication":"https://pith.science/pith/4UTGWXETVTPFUQWA4CZIOPRQ7W/action/replication_record"}},"created_at":"2026-05-18T00:19:26.196346+00:00","updated_at":"2026-05-18T00:19:26.196346+00:00"}