{"paper":{"title":"Equivalence of optimal $L^1$-inequalities on Riemannian Manifolds","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jurandir Ceccon, Leandro Cioletti","submitted_at":"2014-04-11T21:57:23Z","abstract_excerpt":"Let $(M,g)$ be a smooth compact Riemannian manifold of dimension $n \\geq 2$. This paper concerns to the validity of the optimal Riemannian $L^1$-Entropy inequality \\[ {\\bf Ent}_{dv_g}(u) \\leq n \\log \\left(A_{opt} \\|D u\\|_{BV(M)} + B_{opt}\\right) \\] for all $u \\in BV(M)$ with $\\|u\\|_{L^1(M)} = 1$ and existence of extremal functions. In particular, we prove that this optimal inequality is equivalent a optimal $L^1$-Sobolev inequality obtained by Druet [6]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3234","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"}