{"paper":{"title":"Sign-changing blow-up for scalar curvature type equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fr\\'ed\\'eric Robert, J\\'er\\^ome V\\'etois","submitted_at":"2012-10-08T11:42:43Z","abstract_excerpt":"Given $(M,g)$ a compact Riemannian manifold of dimension $n\\geq 3$, we are interested in the existence of blowing-up sign-changing families $(\\ue)_{\\eps>0}\\in C^{2,\\theta}(M)$, $\\theta\\in (0,1)$, of solutions to $$\\Delta_g \\ue+h\\ue=|\\ue|^{\\frac{4}{n-2}-\\eps}\\ue\\hbox{ in }M\\,,$$ where $\\Delta_g:=-\\hbox{div}_g(\\nabla)$ and $h\\in C^{0,\\theta}(M)$ is a potential. We prove that such families exist in two main cases: in small dimension $n\\in \\{3,4,5,6\\}$ for any potential $h$ or in dimension $3\\leq n\\leq 9$ when $h\\equiv\\frac{n-2}{4(n-1)}\\Scal_g$. These examples yield a complete panorama of the comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2244","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"}