{"paper":{"title":"Isoperimetric profile comparisons and Yamabe constants","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":"2010-10-18T16:08:06Z","abstract_excerpt":"We estimate from below the isoperimetric profile of $S^2 \\times \\re^2$ and use this information to obtain lower bounds for the Yamabe constant of $S^2 \\times \\re^2$. This provides a lower bound for the Yamabe invariants of products $S^2 \\times M^2$ for any closed Riemann surface $M$. Explicitly we show that $Y(S^2 \\times M^2) > (2/3) Y(S^4)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3642","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"}