{"paper":{"title":"Scalar Curvature Compactness for Warped Products on $\\mathbb{S}^2\\times\\mathbb{S}^1$ with Varying Base Metrics","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Changliang Wang, Zhixin Wang","submitted_at":"2026-05-24T15:02:38Z","abstract_excerpt":"We study the Gromov--Sormani MinA scalar curvature compactness conjecture for warped product metrics on $\\mathbb{S}^2\\times\\mathbb{S}^1$ of the form introduced by Kazaras-Xu in \\cite{KazarasXu2023} as follows: \\[ g_i=\\varphi_i^{-2}h_i+\\varphi_i^2d\\xi^2, \\qquad h_i=dr^2+u_i^2(r)d\\theta^2. \\] Assuming nonnegative scalar curvature, a uniform volume upper bound, and a positive lower bound for the areas of closed minimal surfaces, we prove a uniform diameter bound for the base surfaces $(\\mathbb{S}^2,h_i)$. Based on this key estimate, we further obtain compactness of the base warping functions $u_i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25116","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25116/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}