{"paper":{"title":"$L^\\infty$-metrics on tori and Schoen's conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jian Wang, Jinmin Wang, Zhizhang Xie","submitted_at":"2026-06-19T11:14:03Z","abstract_excerpt":"We prove Schoen's conjecture on $L^\\infty$-metrics for tori under an additional assumption on the fundamental group of the singular set. More precisely, we consider an $L^\\infty$-metric on a torus that is smooth and has non-negative scalar curvature away from a singular set of Minkowski dimension at most $n-3+(n-1)^{-1}$. We show that if the induced homomorphism from the fundamental group of the singular set to the fundamental group of the torus is not surjective, then this metric extends to a smooth flat metric on the torus. Our proof uses weighted scalar curvature and the relative index theo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21325","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/2606.21325/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"}