{"paper":{"title":"Blowing-up solutions concentrating along minimal submanifolds for some supercritical elliptic problems on Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Anna Maria Micheletti, Marco Ghimenti","submitted_at":"2014-01-21T18:19:13Z","abstract_excerpt":"Let $(M,g)$ and $(K,\\kappa)$ be two Riemannian manifolds of dimensions $m$ and $k ,$ respectively. Let $\\omega\\in C^2(N),$ $\\omega> 0.$\n  The warped product $ M\\times _\\omega K$ is the $ (m+k)$-dimensional product manifold $M\\times K$ furnished with metric $ g+\\omega^2 \\kappa.$ We prove that the supercritical problem $$-\\Delta _{g+\\omega^2 \\kappa}u+h u=u^{ {m+2\\over m-2} \\pm\\varepsilon},\\ u>0,\\ \\hbox{in}\\ (M\\times _\\omega K,g+\\omega^2 \\kappa)$$ has a solution which concentrate along a $k$-dimensional minimal submanifold $\\Gamma$ of $M\\times _\\omega N$ as the real parameter $\\varepsilon$ goes t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5411","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"}