{"paper":{"title":"Orbifold singularity formation along ancient and immortal Ricci flows","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Alix Deruelle, Tristan Ozuch","submitted_at":"2024-10-21T14:54:20Z","abstract_excerpt":"In stark contrast to lower dimensions, we produce a plethora of ancient and immortal Ricci flows in real dimension $4$ with Einstein orbifolds as tangent flows at infinity. For instance, for any $k\\in\\mathbb{N}_0$, we obtain continuous families of non-isometric ancient Ricci flows on $\\#k(\\mathbb{S}^2\\times \\mathbb{S}^2)$ depending on a number of parameters growing linearly in $k$, and a family of half-PIC ancient Ricci flows on $\\mathbb{CP}^2\\#\\mathbb{CP}^2$.\n  The ancient/immortal dichotomy is determined by a notion of linear stability of orbifold singularities with respect to the expected w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.16075","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.16075/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}