{"paper":{"title":"Longtime existence of the K\\\"ahler-Ricci flow on $\\Bbb C ^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Albert Chau, Ka-Fai Li, Luen-fai Tam","submitted_at":"2014-09-05T19:30:21Z","abstract_excerpt":"We produce longtime solutions to the K\\\"ahler-Ricci flow for complete K\\\"ahler metrics on $\\Bbb C ^n$ without assuming the initial metric has bounded curvature, thus extending results in [3]. We prove the existence of a longtime bounded curvature solution emerging from any complete $U(n)$-invariant K\\\"ahler metric with non-negative holomorphic bisectional curvature, and that the solution converges as $t\\to \\infty$ to the standard Euclidean metric after rescaling. We also prove longtime existence results for more general K\\\"ahler metrics on $\\Bbb C ^n$ which are not necessarily $U(n)$-invariant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1906","kind":"arxiv","version":3},"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"}