{"paper":{"title":"On the volume of locally conformally flat 4 dimensional hypersphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Linlin Sun, Qing Cui","submitted_at":"2016-11-02T09:25:08Z","abstract_excerpt":"Let $M$ be a 5 dimensional Riemannian manifold with $Sec_M\\in[0,1]$, $\\Sigma$ be a locally conformally flat hypersphere in $M$ with mean curvature $H$. We prove that, there exists $\\varepsilon_0>0$, such that $\\int_\\Sigma (1+H^2)^2 \\ge 8\\pi^2/3$, provided $H \\le \\varepsilon_0$. In particular, if $\\Sigma$ is a locally conformally flat minimal hypersphere in $M$, then $Vol(\\Sigma) \\ge 8\\pi^2/3$, which partially answer a question proposed by Mazet and Rosenberg \\cite{Ma&Rosen}. For an $(n+1)-$ dimensional rotationally symmetric Riemannian manifold $M$, we show that an immersed hypersurface $\\Sigm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00516","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"}