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The domains \\Omega_j are rotationally symmetric and periodic with respect to the R-axis of the cylinder and as j converges to 0 the domain \\Omega_j converges to the cylinder B^n x R."},"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":"1305.6516","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-28T14:39:44Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"6a4fca27eeb5978012c00582809038268e1b64b90a86fba211e51c6bcf33b082","abstract_canon_sha256":"c796f6c575e88a85da4ab440053706ea0dd3c01bdc7cc928c48a3927b41e81b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:40.563292Z","signature_b64":"T4GcJZ9lgGIlDuzpVdNCsYG+NML8hlZ0lM/56w1q7rAaR40agjoCaLz0wR0Ebu22HK/db4UjmmyOVUCVZ9+fDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a5b127e7e491d4d7440902081283be8870a5c16d99ce2615665ffc7665afbe0","last_reissued_at":"2026-05-18T03:24:40.562586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:40.562586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Delaunay type domains for an overdetermined elliptic problem in S^n x R and H^n x R","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Filippo Morabito, Pieralberto Sicbaldi","submitted_at":"2013-05-28T14:39:44Z","abstract_excerpt":"We prove the existence of a countable family of Delaunay type domains \\Omega_j in M^n x R, where M^n is the Riemannian manifold S^n or H^n and n is at least 2, bifurcating from the cylinder B^n x R (where B^n is a geodesic ball of radius 1 in M^n) for which the first eigenfunction of the Laplace-Beltrami operator with zero Dirichlet boundary condition also has constant Neumann data at the boundary. 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