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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 $p_0$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1606.03661","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-12T03:10:31Z","cross_cats_sorted":[],"title_canon_sha256":"0c83b9e1b90b6abdbb4650a58cc6fc955b7d400668ca599d2f5ff6a3f1cab0af","abstract_canon_sha256":"05559e65df488b2703d41b9b0c1d59eec5cc316a2d776a95f55c1764b0a5daaf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:19.658333Z","signature_b64":"1ELHTRnkqsCK12qkMbJ/fJunWtCfxZDUkzJv9RRw5mVETByQADWZ/uyQ6Ge/xVhzV+Gi7rAs/29R3sx+Sg20Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02b5aec577db2c5aabc3bb8f8a4400237492dc3fd5ea47fc232b67e156b71eb9","last_reissued_at":"2026-05-18T01:12:19.657947Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:19.657947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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":"2016-06-12T03:10:31Z","abstract_excerpt":"Let $(\\mathcal{M}, g)$ be a compact Riemannian manifold of dimension $N\\geq 2$. 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