{"paper":{"title":"A nonlocal $\\mathbf Q$-curvature flow on a class of closed manifolds of dimension $\\mathbf{n \\geq 5}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Xuezhang Chen","submitted_at":"2015-01-04T01:12:32Z","abstract_excerpt":"In this paper, we employ a nonlocal $Q$-curvature flow inspired by Gursky-Malchiodi's work \\cite{gur_mal} to solve the prescribed $Q$-curvature problem on a class of closed manifolds: For $n \\geq 5$, let $(M^n,g_0)$ be a smooth closed manifold, which is not conformally diffeomorphic to the standard sphere, satisfying either Gursky-Malchiodi's semipositivity hypotheses: scalar curvature $R_{g_0}>0$ and $Q_{g_0} \\geq 0$ not identically zero or Hang-Yang's: Yamabe constant $Y(g_0)>0$, Paneitz-Sobolev constant $q(g_0)>0$ and $Q_{g_0} \\geq 0$ not identically zero. Let $f$ be a smooth positive funct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00618","kind":"arxiv","version":3},"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"}