{"work":{"id":"3f51048e-ac27-40e7-8a59-ac4755852437","openalex_id":null,"doi":null,"arxiv_id":"math/0307245","raw_key":null,"title":"Finite extinction time for the solutions to the Ricci flow on certain three-manifolds","authors":null,"authors_text":"Grisha Perelman","year":2003,"venue":"math.DG","abstract":"Let M be a closed oriented three-manifold, whose prime decomposition contains no aspherical factors. We show that for any initial riemannian metric on M the solution to the Ricci flow with surgery, defined in our previous paper math.DG/0303109, becomes extinct in finite time. The proof uses a version of the minimal disk argument from 1999 paper by Richard Hamilton, and a regularization of the curve shortening flow, worked out by Altschuler and Grayson.","external_url":"https://arxiv.org/abs/math/0307245","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-05-25T02:46:33.725469+00:00","pith_arxiv_id":"math/0307245","created_at":"2026-05-09T06:30:44.513650+00:00","updated_at":"2026-06-05T21:23:00.469572+00:00","title_quality_ok":true,"display_title":"Finite extinction time for the solutions to the Ricci flow on certain three-manifolds","render_title":"Finite extinction time for the solutions to the Ricci flow on certain three-manifolds"},"hub":{"state":{"work_id":"3f51048e-ac27-40e7-8a59-ac4755852437","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":16,"external_cited_by_count":null,"distinct_field_count":5,"first_pith_cited_at":"2023-02-09T22:42:36+00:00","last_pith_cited_at":"2026-05-22T14:27:32+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-06-29T21:09:14.618155+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":2}],"polarity_counts":[{"context_polarity":"background","n":2}],"runs":{},"summary":{},"graph":{},"authors":[]}}