{"paper":{"title":"Ancient solutions for flow by powers of the curvature in $\\mathbb R^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alina Stancu, Guofang Wei, Julie Clutterbuck, Theodora Bourni, Valentina-Mira Wheeler, Xuan Hien Nguyen","submitted_at":"2020-05-15T16:55:16Z","abstract_excerpt":"We construct a new compact convex embedded ancient solution of the $\\kappa^\\alpha$ flow in $\\mathbb R^2$, $\\alpha\\in(\\frac12,1)$ that lies between two parallel lines. Using this solution we classify all convex ancient solutions of the $\\kappa^\\alpha$ flow in $\\mathbb R^2$, for $\\alpha\\in(\\frac23,1)$. Moreover, we show that any non-compact convex embedded ancient solution of the $\\kappa^\\alpha$ flow in $\\mathbb R^2$, $\\alpha\\in(\\frac12,1)$ must be a translating solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.07642","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/2005.07642/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"}