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We show that the Euclidean cone over an n-dimensional Riemannian manifold whose Ricci curvature is bounded from below by n-1 satisfies the curvature-dimension condition CD(0; n+1) and that the spherical cone over the same manifold fulfills the curvature-dimension condition CD(n; n+1). More generally, for each N > 1 we prove that the condition CD(N-1;N) for a wei"},"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":"1103.0197","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-01T15:27:37Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"fd7def4119c7fce2c8ca4623e9a4bed992dc8a9620dc80aae3ce6758cdb307b3","abstract_canon_sha256":"3734c1fba5867583b313532c54798264e78293d734fccaeb20cfb5313e17eeb0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:37.129158Z","signature_b64":"uE1T0Vtv5s3I34UAyYCyPOMD33wfx7GEcFjOQh1vOUOzxEzxjeS+6hhLVhWorrYi+Yo8RvrnZWKPofQ6rQ7IBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0380c020506293a19cd7577b1bd77e61e9d12f105f4f89f7507fb034274981a8","last_reissued_at":"2026-05-18T04:27:37.128499Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:37.128499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ricci Bounds for Euclidean and Spherical Cones (revised/extended version)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Karl-Theodor Sturm, Kathrin Bacher","submitted_at":"2011-03-01T15:27:37Z","abstract_excerpt":"We prove generalized lower Ricci bounds for Euclidean and spherical cones over complete Riemannian manifolds. 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