{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FD3U4CWMOV7JILFJHHVFDIGOG7","short_pith_number":"pith:FD3U4CWM","schema_version":"1.0","canonical_sha256":"28f74e0acc757e942ca939ea51a0ce37da42771a4246cfd0918c90290c9b955a","source":{"kind":"arxiv","id":"1605.07963","version":1},"attestation_state":"computed","paper":{"title":"Mean curvature flow of arbitrary codimension in complex projective spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hongwei Xu, Li Lei","submitted_at":"2016-05-25T16:56:12Z","abstract_excerpt":"In this paper, we investigate the mean curvature flow of submanifolds of arbitrary codimension in $\\mathbb{C}\\mathbb{P}^m$. We prove that if the initial submanifold satisfies a pinching condition, then the mean curvature flow converges to a round point in finite time, or converges to a totally geodesic submanifold as $t \\rightarrow \\infty$. Consequently, we obtain a new differentiable sphere theorem for submanifolds in $\\mathbb{C}\\mathbb{P}^m$. Our work improves the convergence theorem for mean curvature flow due to Pipoli and Sinestrari {\\cite{PiSi2015}}."},"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":"1605.07963","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-05-25T16:56:12Z","cross_cats_sorted":[],"title_canon_sha256":"4451dd4b526a5eb462a33c7fbdfec6f7fdf8e17a31e432e226e3abc2949dc00f","abstract_canon_sha256":"7d4e78bbee6098e9aa70966591f11800798144e53e3fdc6a6de2938383ddb8e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:38.699874Z","signature_b64":"mvaQ6DLOpvkFozuGRQJrNInOsuCjDms7KODhCn0buZTCxBHiTfoj8E1o/y5S5S3i3xpTXcm+Q9LiGqYEJxy1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28f74e0acc757e942ca939ea51a0ce37da42771a4246cfd0918c90290c9b955a","last_reissued_at":"2026-05-18T01:13:38.699177Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:38.699177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mean curvature flow of arbitrary codimension in complex projective spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hongwei Xu, Li Lei","submitted_at":"2016-05-25T16:56:12Z","abstract_excerpt":"In this paper, we investigate the mean curvature flow of submanifolds of arbitrary codimension in $\\mathbb{C}\\mathbb{P}^m$. We prove that if the initial submanifold satisfies a pinching condition, then the mean curvature flow converges to a round point in finite time, or converges to a totally geodesic submanifold as $t \\rightarrow \\infty$. Consequently, we obtain a new differentiable sphere theorem for submanifolds in $\\mathbb{C}\\mathbb{P}^m$. Our work improves the convergence theorem for mean curvature flow due to Pipoli and Sinestrari {\\cite{PiSi2015}}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07963","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":"1605.07963","created_at":"2026-05-18T01:13:38.699279+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.07963v1","created_at":"2026-05-18T01:13:38.699279+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07963","created_at":"2026-05-18T01:13:38.699279+00:00"},{"alias_kind":"pith_short_12","alias_value":"FD3U4CWMOV7J","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FD3U4CWMOV7JILFJ","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FD3U4CWM","created_at":"2026-05-18T12:30:15.759754+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/FD3U4CWMOV7JILFJHHVFDIGOG7","json":"https://pith.science/pith/FD3U4CWMOV7JILFJHHVFDIGOG7.json","graph_json":"https://pith.science/api/pith-number/FD3U4CWMOV7JILFJHHVFDIGOG7/graph.json","events_json":"https://pith.science/api/pith-number/FD3U4CWMOV7JILFJHHVFDIGOG7/events.json","paper":"https://pith.science/paper/FD3U4CWM"},"agent_actions":{"view_html":"https://pith.science/pith/FD3U4CWMOV7JILFJHHVFDIGOG7","download_json":"https://pith.science/pith/FD3U4CWMOV7JILFJHHVFDIGOG7.json","view_paper":"https://pith.science/paper/FD3U4CWM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.07963&json=true","fetch_graph":"https://pith.science/api/pith-number/FD3U4CWMOV7JILFJHHVFDIGOG7/graph.json","fetch_events":"https://pith.science/api/pith-number/FD3U4CWMOV7JILFJHHVFDIGOG7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FD3U4CWMOV7JILFJHHVFDIGOG7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FD3U4CWMOV7JILFJHHVFDIGOG7/action/storage_attestation","attest_author":"https://pith.science/pith/FD3U4CWMOV7JILFJHHVFDIGOG7/action/author_attestation","sign_citation":"https://pith.science/pith/FD3U4CWMOV7JILFJHHVFDIGOG7/action/citation_signature","submit_replication":"https://pith.science/pith/FD3U4CWMOV7JILFJHHVFDIGOG7/action/replication_record"}},"created_at":"2026-05-18T01:13:38.699279+00:00","updated_at":"2026-05-18T01:13:38.699279+00:00"}