{"paper":{"title":"On the Yamabe constants of $S^2 \\times \\re^3$ and $S^3 \\times \\re^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jimmy Petean, Juan Miguel Ruiz","submitted_at":"2012-02-06T00:38:18Z","abstract_excerpt":"We compare the isoperimetric profiles of $S^2 \\times \\re^3$ and of $S^3 \\times \\re^2$ with that of a round 5-sphere (of appropriate radius). Then we use this comparison to obtain lower bounds for the Yamabe constants of $S^2 \\times \\re^3$ and $S^3 \\times \\re^2$. Explicitly we show that $Y(S^3 \\times \\re^2, [g_0^3 +dx^2]) > (3 /4) Y(S^5)$ and $Y(S^2 \\times \\re^3, [g_0^2 +dx^2]) > 0.63 Y(S^5)$. We also obtain explicit lower bounds in higher dimensions and for products of Euclidean space with a closed manifold of positive Ricci curvature. The techniques are a more general version of those used by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1022","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"}