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The existence time depends on initial data $u_0$ and the metric $\\omega$. As a corollary, we get that Calabi flow has short time"},"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":"1701.06943","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-01-24T15:47:23Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"af3a8755f88899170e03f65747b96b5b3e6553e16af51ac61513e7dcb6811704","abstract_canon_sha256":"40d3c434e03063ac4375a32f5bde6caec2eca99ade687a577033f771b9e287d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:09.076054Z","signature_b64":"/8yWfWInfakSSqCzi0oPc79KSxABliIawfz43iAQ6A5/hwqH5nOKQ7Umq2w4mXE8l2L4A+akGqZtE1x8LWddDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfc9ef0d95761e966cf5c5a38313e3854c0b85ee0c102eb112ba7393d7f9803e","last_reissued_at":"2026-05-18T00:50:09.075372Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:09.075372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Calabi flow with rough initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Weiyong He, Yu Zeng","submitted_at":"2017-01-24T15:47:23Z","abstract_excerpt":"In this paper, we prove that there exists a dimensional constant $\\delta > 0$ such that given any background K\\\"ahler metric $\\omega$, the Calabi flow with initial data $u_0$ satisfying \\begin{equation*} \\partial \\bar \\partial u_0 \\in L^\\infty (M) \\text{ and } (1- \\delta )\\omega < \\omega_{u_0} < (1+\\delta )\\omega, \\end{equation*} admits a unique short time solution and it becomes smooth immediately, where $\\omega_{u_0} : = \\omega +\\sqrt{-1}\\partial \\bar\\partial u_0$. The existence time depends on initial data $u_0$ and the metric $\\omega$. 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