{
  "abstract": "Let $3\\leq n\\leq7$, $2\\leq k\\leq n-1$, and $m=n-k-1$. We prove that a complete, connected, noncompact spin manifold $(M^n,g)$ with scalar curvature $R_M\\geq k(k-1)$ is isometric to $\\mathbb{S}^k\\times\\mathbb{T}^m_Λ\\times\\mathbb{R}$ if it admits a smooth proper map of nonzero degree to $\\mathbb{S}^k\\times\\mathbb{T}^m\\times\\mathbb{R}$ whose spherical component is 1-Lipschitz. The flat torus in the conclusion is not necessarily isometric to the target torus.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20498",
  "author_total": 1,
  "authors": [
    {
      "name": "Guangrui Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eg3g9vv2wkzff.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20498",
  "fulltext_url": null,
  "id": "eg3g9vv2wkzff",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20498",
  "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": "W7213599972",
  "pdf_url": "https://arxiv.org/pdf/2609.20498",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eg3g9vv2wkzff.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20498",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20498"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Llarull type theorem on complete non-compact manifolds",
  "title_text": "A Llarull type theorem on complete non-compact manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/eg3g9vv2wkzff",
  "venue": "arXiv",
  "versions": []
}