{"paper":{"title":"Overdetermined problems and constant mean curvature surfaces in cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filomena Pacella, Giulio Tralli","submitted_at":"2018-02-09T10:45:54Z","abstract_excerpt":"We consider a partially overdetermined problem in a sector-like domain $\\Omega$ in a cone $\\Sigma$ in $\\mathbb{R}^N$, $N\\geq 2$, and prove a rigidity result of Serrin type by showing that the existence of a solution implies that $\\Omega$ is a spherical sector, under a convexity assumption on the cone. We also consider the related question of characterizing constant mean curvature compact surfaces $\\Gamma$ with boundary which satisfy a \"gluing\" condition with respect to the cone $\\Sigma$. We prove that if either the cone is convex or the surface is a radial graph then $\\Gamma$ must be a spheric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03197","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"}