{"paper":{"title":"A characterization of round spheres in space forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Francisco Fontenele, Roberto Alonso N\\'u\\~nez","submitted_at":"2017-06-14T19:22:33Z","abstract_excerpt":"Let $\\mathbb Q^{n+1}_c$ be the complete simply-connected $(n+1)$-dimensional space form of curvature $c$. In this paper we obtain a new characterization of geodesic spheres in $\\mathbb Q^{n+1}_c$ in terms of the higher order mean curvatures. In particular, we prove that the geodesic sphere is the only complete bounded immersed hypersurface in $\\mathbb Q^{n+1}_c,\\;c\\leq 0,$ with constant mean curvature and constant scalar curvature. The proof relies on the well known Omori-Yau maximum principle, a formula of Walter for the Laplacian of the $r$-th mean curvature of a hypersurface in a space form"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04644","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"}