{
  "abstract": "We prove Schoen's conjecture on $L^\\infty$-metrics for tori. More precisely, we show that any $L^\\infty$-metric on a torus that is smooth and has non-negative scalar curvature away from an embedded submanifold with codimension at least three extends to a smooth flat metric. We also prove a LLarull-type theorem for $L^\\infty$-metric. Our proof uses weighted scalar curvature and the relative index theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.21325",
  "author_total": 3,
  "authors": [
    {
      "name": "Jian Wang"
    },
    {
      "name": "Jinmin Wang"
    },
    {
      "name": "Zhizhang Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/emh74cj5p3tkq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.21325",
  "fulltext_url": null,
  "id": "emh74cj5p3tkq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.21325",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7165634500",
  "pdf_url": "https://arxiv.org/pdf/2606.21325",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/emh74cj5p3tkq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2606.21325",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.21325"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "$L^\\infty$-metrics on tori and Schoen's conjecture",
  "title_text": "L^∞-metrics on tori and Schoen's conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/emh74cj5p3tkq",
  "venue": "arXiv",
  "versions": []
}