{"paper":{"title":"Sharp L^p-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":"2013-07-26T18:08:10Z","abstract_excerpt":"\\small{In 2004, Del Pino and Dolbeault \\cite{DPDo} and Gentil \\cite{G} investigated, independently, best constants and extremals associated to sharp Euclidean $L^p$-entropy inequalities. In this work, we present some important advances in the Riemannian context. Namely, let $(M,g)$ be a compact Riemannian manifold of dimension $n \\geq 3$. For $1 < p \\leq 2$, we prove that the sharp Riemannian $L^p$-entropy inequality\n  \\[\\int_M |u|^p \\log(|u|^p) dv_g \\leq \\frac{n}{p} \\log ({\\cal A}_{opt} \\int_M |\\nabla u|_g^p dv_g + {\\cal B}) \\]\n  \\n holds on all functions $u \\in H^{1,p}(M)$ such that $||u||_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7115","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"}