{"paper":{"title":"Geometric convergence of the K\\\"ahler-Ricci flow on complex surfaces of general type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Ben Weinkove, Bin Guo, Jian Song","submitted_at":"2015-05-04T16:50:28Z","abstract_excerpt":"We show that on smooth minimal surfaces of general type, the K\\\"ahler-Ricci flow starting at any initial K\\\"ahler metric converges in the Gromov-Hausdorff sense to a K\\\"ahler-Einstein orbifold surface. In particular, the diameter of the evolving metrics is uniformly bounded for all time and the K\\\"ahler-Ricci flow contracts all the holomorphic spheres with $(-2)$ self-intersection number to isolated orbifold points. Our estimates do not require a priori the existence of an orbifold K\\\"ahler-Einstein metric on the canonical model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00705","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"}