{"paper":{"title":"Some results on Chern's problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Qi Ding, Y.L. Xin","submitted_at":"2010-12-06T04:37:44Z","abstract_excerpt":"For a compact minimal hypersurface $M$ in $S^{n+1}$ with the squared length of the second fundamental form $S$ we confirm that there exists a positive constant $\\de(n)$ depending only on $n,$ such that if $n\\leq S\\leq n +\\delta(n)$, then $S\\equiv n$, i.e., $M$ is a Clifford minimal hypersurface, in particular, when $n\\ge 6,$ the pinching constant $\\de(n)=\\f{n}{23}.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1073","kind":"arxiv","version":1},"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"}