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This paper concerns to the validity of the optimal Gagliardo-Nirenberg inequality\n  (\\int_M |u|^r\\; dv_g)^{\\frac{\\tau}{r \\theta}} \\leq (A_{opt} (\\int_M |\\nabla_g u|^p\\; dv_g)^{\\frac{\\tau}{p}} + B_{opt} (\\int_M |u|^p\\; dv_g)^{\\frac{\\tau}{p}}) (int_M |u|^q\\; dv_g)^{\\frac{\\tau(1 - \\theta)}{\\theta q}} \\; .\n  This kind of inequality is studied in Chen and Sun (Nonlinear Analysis 72 (2010), pp. 3159-3172) where the authors established its validity when 2 <"},"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":"1307.8039","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-30T16:43:18Z","cross_cats_sorted":[],"title_canon_sha256":"c3a405a49e5e8802635506a83b177d4f98a1d1806e8f78826808515348d8a80f","abstract_canon_sha256":"3d1059d5f1f7fd49bf19fb44f2694ec7d4d914a0c0d4b2f0ff344528c2e04c32"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:21.050485Z","signature_b64":"kkfTbMCi/naj9vb0ExkjdJR4gG0TztCuW6/r42HOcpRIyPmSrtbV02dknW6SPA3WlDqNNsfz8tpin2ZM2ngRAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10f2d2fbe7af7faf1e53f3233bd30c9f35faaf138857595612d03f83d3b98215","last_reissued_at":"2026-05-18T01:36:21.049913Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:21.049913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp constant in Riemannian L^p-Gagliardo-Nirenberg inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carlos Duran, Jurandir Ceccon","submitted_at":"2013-07-30T16:43:18Z","abstract_excerpt":"Let (M,g) be a smooth compact Riemannian manifold of dimension n \\geq 2, 1 < p < n and 1 \\leq q < r < p^\\ast = \\frac{np}{n-p} be real parameters. 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