{"paper":{"title":"Isoperimetric regions in spherical cones and Yamabe constants of $M\\times S^1$","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jimmy Petean","submitted_at":"2007-10-12T19:42:16Z","abstract_excerpt":"Given closed Riemannian manifold $(M^n, g)$ of positive Ricci curvature $Ricci(g) \\geq (n-1)g$ we study isoperimetric regions on the spherical cone over $M$. When $g$ is Einstein we use this to compute the Yamabe constant of $(M \\times {\\bf R}, g + dt^2)$ and so to obtain lower bounds for the Yamabe invariant of $M\\times S^1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.2536","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"}