{"paper":{"title":"Some sharp differential sphere theorems for nonnegative scalar curvature manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Linlin Sun, Qing Cui","submitted_at":"2017-08-31T08:46:40Z","abstract_excerpt":"In this paper, we obtain several new intrinsic and extrinsic differential sphere theorems via Ricci flow.\n  For intrinsic case, we show that a closed simply connected $n(\\ge 4)$-dimensional Riemannian\n  manifold $M$ is diffeomorphic to $S^n$\n  if one of the following\n  conditions holds pointwisely: $$\n  (i)\\ R_0>\\left(1-\\frac{24(\\sqrt{10}-3)}{n(n-1)}\\right)K_{max};\\quad\n  \\ (ii)\\ \\frac{Ric^{[4]}}{4(n-1)}>\\left(1-\\frac{6(\\sqrt{10}-3)}{n-1}\\right)K_{max}.$$\n  Here $K_{max}$, $Ric^{[k]}$ and $R_0$ stand for the maximal sectional curvature,\n  the $k$-th weak Ricci curvature and\n  the normalized sc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09618","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"}