{"paper":{"title":"K\\\"ahler Ricci flow with vanished Futaki invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Zhenlei Zhang","submitted_at":"2010-11-22T13:14:52Z","abstract_excerpt":"We study the convergence of the K\\\"ahler-Ricci flow on a compact K\\\"ahler manifold $(M,J)$ with positive first Chern class $c_1(M;J)$ and vanished Futaki invariant on $\\pi c_1(M;J)$. As the application we establish a criterion for the stability of the K\\\"ahler-Ricci flow (with perturbed complex structure) around a K\\\"ahler-Einstein metric with positive scalar curvature, under certain local stable condition on the dimension of holomorphic vector fields. In particular this gives a stability theorem for the existence of K\\\"ahler-Einstein metrics on a K\\\"ahler manifold with possibly nontrivial hol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4799","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"}