{"paper":{"title":"Regularity of K\\\"ahler-Ricci flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Gang Tian, Zhenlei Zhang","submitted_at":"2013-04-09T16:35:33Z","abstract_excerpt":"In this short note we announce a regularity theorem for K\\\"ahler-Ricci flow on a compact Fano manifold (K\\\"ahler manifold with positive first Chern class) and its application to the limiting behavior of K\\\"ahler-Ricci flow on Fano 3-manifolds. Moreover, we also present a partial $C^0$ estimate to the K\\\"ahler-Ricci flow under the regularity assumption, which extends previous works on K\\\"ahler-Einstein metrics and shrinking K\\\"ahler-Ricci solitons (cf. \\cite{Ti90}, \\cite{DoSu12}, \\cite{Ti12}, \\cite{PSS12}). The detailed proof will appear in \\cite{TiZh13}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2651","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"}