{"paper":{"title":"Serrin's over-determined Problem on Riemannian Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ignace Aristide Minlend, Mouhamed Moustapha Fall","submitted_at":"2014-05-31T10:35:51Z","abstract_excerpt":"Let $(\\mathcal{M},g)$ be a compact Riemannian manifold of dimension $N$, $N\\geq 2$. In this paper, we prove that there exists a family of domains $(\\Omega_\\varepsilon)_{\\varepsilon\\in(0,\\varepsilon_0)}$ and functions $u_\\varepsilon$ such that $ -\\Delta_{g} u_\\varepsilon=1 \\quad \\textrm{ in } \\Omega_\\varepsilon, \\quad u_\\varepsilon=0 \\quad\\textrm{ on }\\partial\\Omega_\\varepsilon, \\quad\n  {g}(\\nabla_{ {g}} {u_\\varepsilon}, {\\nu}_\\varepsilon)=-\\frac{\\varepsilon}{N} \\quad \\textrm{ on }\\partial\\Omega_\\varepsilon, $ where $\\nu_\\varepsilon$ is the unit outer normal of $\\partial\\Omega_\\varepsilon$. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0065","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"}