{"paper":{"title":"Existence of Self-Cheeger sets on Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ignace Aristide Minlend","submitted_at":"2016-03-01T09:58:44Z","abstract_excerpt":"Let $(\\mathcal{M},g)$ be a compact Riemannian manifold of dimension $N\\geq 2$. We prove the existence of a family $(\\Omega_\\varepsilon)_{\\varepsilon\\in (0,\\varepsilon_0)}$ of self-Cheeger sets in $(\\mathcal{M},g)$ . The domains $\\Omega_\\varepsilon\\subset\\mathcal{M}$ are perturbations of geodesic balls of radius $\\varepsilon$ centered at $p \\in \\mathcal{M}$, and in particular, if $p_0$ is a non-degenerate critical point of the scalar curvature of $g$, then the family $(\\partial \\Omega_\\varepsilon)_{\\varepsilon \\in (0,\\varepsilon_0)}$ constitutes a smooth foliation of a neighborhood of $p_0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00204","kind":"arxiv","version":3},"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"}