{
  "abstract": "We establish integral extension criteria for the Laplacian flow of closed $G_2$-structures on compact $7$-dimensional manifolds $M$. Assuming a uniform lower bound for the scalar curvature, we prove that a finite-time solution extends smoothly whenever the spatial $L^p$ norm of the $77$-dimensional Weyl component $W_{77}$ remains uniformly bounded for some $p\\ge 7/2$. We also obtain a mixed space--time extension criterion under the condition \\[ W_{77}\\in L^q(0,T;L^p(M,g(t))), \\qquad \\frac{7}{2}<p<\\infty,\\quad 1\\le q<\\infty,\\quad \\frac{1}{q}+\\frac{7}{p}\\le 2. \\] In particular, finite space-time $L^4$ integrability of $W_{77}$ is sufficient for extension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23412",
  "author_total": 3,
  "authors": [
    {
      "name": "Chuanhuan Li"
    },
    {
      "name": "Yi Li"
    },
    {
      "name": "Kai Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/55eq77w0vyn91.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23412",
  "fulltext_url": null,
  "id": "55eq77w0vyn91",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23412",
  "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": "W7222946053",
  "pdf_url": "https://arxiv.org/pdf/2610.23412",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/55eq77w0vyn91.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23412",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23412"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Long-time existence of the Laplacian flow with Weyl tensor",
  "title_text": "Long-time existence of the Laplacian flow with Weyl tensor",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/55eq77w0vyn91",
  "venue": "arXiv",
  "versions": []
}