{"paper":{"title":"On Area-preserving and Length-preserving Nonlocal Flow of Convex Closed Plane Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Dong-Ho Tsai, Xiao-Liu Wang","submitted_at":"2014-08-08T10:20:56Z","abstract_excerpt":"For any $\\alpha>0,$ we study $k^{\\alpha}$-type length-preserving and area-preserving nonlocal flow of convex closed plane curves and show that these two types of flow evolve such curves into round circles in $C^{\\infty}% $-norm.$\\ $Other relevant $k^{\\alpha}$-type nonlocal flow is also discussed when $\\alpha\\geq1.\\ $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1805","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":""},"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"}