{"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 $\\omega$. As a corollary, we get that Calabi flow has short time"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06943","kind":"arxiv","version":2},"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"}