{"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. Moreover, we prove that the first b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02440","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}