{"paper":{"title":"A remark on an overdetermined problem in Riemannian Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Giulio Ciraolo, Luigi Vezzoni","submitted_at":"2015-12-24T08:31:35Z","abstract_excerpt":"Let $(M,g)$ be a Riemannian manifold with a distinguished point $O$ and assume that the geodesic distance $d$ from $O$ is an isoparametric function. Let $\\Omega\\subset M$ be a bounded domain, with $O \\in \\Omega$, and consider the problem $\\Delta_p u = -1$ in $\\Omega$ with $u=0$ on $\\partial \\Omega$, where $\\Delta_p$ is the $p$-Laplacian of $g$. We prove that if the normal derivative $\\partial_{\\nu}u$ of $u$ along the boundary of $\\Omega$ is a function of $d$ satisfying suitable conditions, then $\\Omega$ must be a geodesic ball. In particular, our result applies to open balls of $\\mathbb{R}^n$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07752","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"}