{"paper":{"title":"On the Best Constant in the Moser-Onofri-Aubin Inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chang-shou Lin, Nassif Ghoussoub","submitted_at":"2009-10-05T23:49:39Z","abstract_excerpt":"Let $S^2$ be the 2-dimensional unit sphere and let $J_\\alpha $ denote the nonlinear functional on the Sobolev space $H^{1,2}(S^2)$ defined by $$ J_\\alpha(u) = \\frac{\\alpha}{4}\\int_{S^2}|\\nabla u|^2 d\\omega + \\int_{S^2} u d\\omega -\\ln \\int_{S^2} e^{u} d\\omega, $$ where $d\\omega$ denotes Lebesgue measure on $S^2$, normalized so that $\\int_{S^2} d\\omega = 1$. Onofri had established that $J_\\alpha$ is non-negative on $H^1(S^2)$ provided $\\alpha \\geq 1$. In this note, we show that if $J_\\alpha$ is restricted to those $u\\in H^1(S^2)$ that satisfy the Aubin condition: \\int_{S^2}e^u x_j dw=0\\quad\\text"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.0890","kind":"arxiv","version":1},"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"}