{"paper":{"title":"On Stable Hypersurfaces with Vanishing Scalar Curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Greg\\'orio Silva Neto","submitted_at":"2013-05-24T18:26:31Z","abstract_excerpt":"We will prove that \\emph{there are no stable complete hypersurfaces of $\\mathbb{R}^4$ with zero scalar curvature, polynomial volume growth and such that $\\dfrac{(-K)}{H^3}\\geq c>0$ everywhere, for some constant $c>0$}, where $K$ denotes the Gauss-Kronecker curvature and $H$ denotes the mean curvature of the immersion. Our second result is the Bernstein type one \\emph{there is no entire graphs of $\\mathbb{R}^4$ with zero scalar curvature such that $\\dfrac{(-K)}{H^3}\\geq c>0$ everywhere}. At last, it will be proved that, if there exists a stable hypersurface with zero scalar curvature and $\\dfra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5819","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"}