{"paper":{"title":"On the long time behaviour of the Conical K\\\"ahler- Ricci flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Xiuxiong Chen, Yuanqi Wang","submitted_at":"2014-02-26T20:55:22Z","abstract_excerpt":"We prove that the conical K\\\"ahler-Ricci flows introduced in \\cite{CYW} exist for all time $t\\in [0,+\\infty)$. These immortal flows possess maximal regularity in the conical category. As an application, we show if the twisted first Chern class $C_{1,\\beta}$ is negative or zero, the corresponding conical K\\\"ahler-Ricci flows converge to K\\\"ahler-Einstein metrics with conical singularities exponentially fast. To establish these results, one of our key steps is to prove a Liouville type theorem for K\\\"ahler-Ricci flat metrics (which are defined over $\\mathbb{C}^{n}$) with conical singularities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6689","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"}