{"paper":{"title":"Collapsing of Products Along the K\\\"ahler-Ricci Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Matthew Gill","submitted_at":"2012-03-16T18:56:54Z","abstract_excerpt":"Let $X = M \\times E$ where $M$ is an $m$-dimensional K\\\"ahler manifold with negative first Chern class and $E$ is an $n$-dimensional complex torus. We obtain $C^\\infty$ convergence of the normalized K\\\"ahler-Ricci flow on $X$ to a K\\\"ahler-Einstein metric on $M$. This strengthens a convergence result of Song-Weinkove and confirms their conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3781","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"}