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For 1 < p <= 2, we establish the validity of the sharp Riemannian Lp-entropy inequality\n  int_M |u|^p log(|u|^p) dv_g <= n/p log ( A_{opt} int_M |Grad_g u|^p dv_g + B )\n  on all functions u em H^{1,p}(M) such that ||u||_{Lp(M)} = 1 for some constant B. Moreover, we prove that the first b"},"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":"1505.02440","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-10T21:28:08Z","cross_cats_sorted":[],"title_canon_sha256":"45cbe21a357e4d7f16bd0b3d5167e56b46b32924bd005a1e7f8ee110ce5002d6","abstract_canon_sha256":"44a957c483d250f3c1577c8b90d8a484378391a3612ff554295e1096e3a2236a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:23.081807Z","signature_b64":"0edHIiKTf52hcQJdKhSUqDbVawqHei1yF4H+BTJ0YaXiRHqI9xUDY84vp/7QOaKBHGtKgCyaxgnrjOyndNwxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c47dbc19485476bd834c3a7e2ffc41a5ba5cfaf018587242787ff5dd2981669","last_reissued_at":"2026-05-18T01:21:23.081199Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:23.081199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp Lp-entropy inequalities on manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jurandir Ceccon, Marcos Montenegro","submitted_at":"2015-05-10T21:28:08Z","abstract_excerpt":"In 2003, Del Pino and Dolbeault [14] and Gentil [19] investigated, independently, best constants and extremals associated to Euclidean Lp-entropy inequalities for p > 1. In this work, we present some contributions in the Riemannian context. Namely, let (M,g) be a closed Riemannian manifold of dimension n >= 3. For 1 < p <= 2, we establish the validity of the sharp Riemannian Lp-entropy inequality\n  int_M |u|^p log(|u|^p) dv_g <= n/p log ( A_{opt} int_M |Grad_g u|^p dv_g + B )\n  on all functions u em H^{1,p}(M) such that ||u||_{Lp(M)} = 1 for some constant B. 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