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We prove the following results in both cases:\n  $\\bullet$ If $(M,g)$ is a {\\it Cartan-Hadamard manifold} which verifies the $n-$dimensional Cartan-Hadamard conjecture, sharp Morrey-Sobolev inequalities hold on $(M,g)$. Moreover, extremals exist if and only if $(M,g)$ is isometric to the standard Euclidean space $(\\mathbb R^n,e)$.\n  $\\bullet$ If $(M,g)$ has {\\it non-negative Ricci curvature}, $(M,g)$ supports the sharp "},"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":"1408.1308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-06T14:54:47Z","cross_cats_sorted":[],"title_canon_sha256":"5912777e7aae65d83c6fa59925e867451a98070a88c67da78a10f9efe282e9a1","abstract_canon_sha256":"586f34c2326671144e430e2b0b87708a18fea22bd7ec4d8bbd6568da4488cddd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:57.024991Z","signature_b64":"GYPGxDLIos1zJo+sIFCgrhArLiL0QYxtKvGA0r2rFYKZBdQMKhac/BuZWqaLByFqjutcJsgum4tKrm7HmNSaAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"001f1f4a27fc40f94b7f059d83c1afbd5f111b0ee484eed2415672b137003815","last_reissued_at":"2026-05-18T02:27:57.024422Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:57.024422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp Morrey-Sobolev inequalities on complete Riemannian Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexandru Krist\\'aly","submitted_at":"2014-08-06T14:54:47Z","abstract_excerpt":"Two Morrey-Sobolev inequalities (with support-bound and $L^1-$bound, respectively) are investigated on complete Riemannian manifolds with their sharp constants in $\\mathbb R^n$. We prove the following results in both cases:\n  $\\bullet$ If $(M,g)$ is a {\\it Cartan-Hadamard manifold} which verifies the $n-$dimensional Cartan-Hadamard conjecture, sharp Morrey-Sobolev inequalities hold on $(M,g)$. 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