{
  "abstract": "In this paper, we give a new proof of Perelman's pseudolocality theorem for Ricci flow, which does not rely on Perelman's Harnack-type inequality. The key step is an estimate relating initial local $μ$-entropy to pointed Nash entropy at later spacetime points. The argument also works for other reasonable geometric flows, like the $G_2$-Laplacian flow, at a scale depending on its deviation from Ricci flow and its scalar curvature lower bound. As a consequence, we can also prove the quantitative rigidity results concerning pointed Nash entropy due to Hein-Naber and Bamler for such geometric flows. In the appendix, we also show that the other results in Bamler's work (arXiv:2008.07093), when suitably modified, remain valid for Laplacian flow with bounded torsion. These include log-Sobolev/Poincaré inequality for conjugate heat kernel measure, heat kernel estimates, and dependence of the pointed Nash entropy on its basepoint.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38408",
  "author_total": 2,
  "authors": [
    {
      "name": "Weiyong He"
    },
    {
      "name": "Longhuan Yan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fszy9v6vrv2cb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38408",
  "fulltext_url": null,
  "id": "fszy9v6vrv2cb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38408",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38408",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fszy9v6vrv2cb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38408",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38408"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Pseudolocality of $G_2$-Laplacian Flow",
  "title_text": "Pseudolocality of G_2-Laplacian Flow",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/fszy9v6vrv2cb",
  "venue": "arXiv",
  "versions": []
}