{
  "abstract": "In a recent breakthrough, Bamler-Lai proved the mean-convex neighborhood conjecture in all dimensions by showing that any nontrivial ancient asymptotically cylindrical mean curvature flow is -- up to splitting Euclidean factors -- either a translating bowl, or an ancient oval, or a translating oval-bowl. In this paper, we provide a short alternative argument for two of the three scenarios. Specifically, using more elementary/traditional methods, we show that if the convergence to the round cylinder is fast then the solution is a bowl times a Euclidean factor, and if the convergence is slow then the solution is an ancient oval. Moreover, the present paper also yields a new proof of the mean-convex neighborhood conjecture for neck-singularities that substantially simplifies and streamlines the approach from our prior work joint with Hershkovits (Acta '22) and Hershkovits-White (Inventiones '22).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30787",
  "author_total": 2,
  "authors": [
    {
      "name": "Kyeongsu Choi"
    },
    {
      "name": "Robert Haslhofer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/czk56c8a2nz5d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30787",
  "fulltext_url": null,
  "id": "czk56c8a2nz5d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30787",
  "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.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7204936852",
  "pdf_url": "https://arxiv.org/pdf/2608.30787",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/czk56c8a2nz5d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30787",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30787"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Ancient cylindrical flows with fast or slow convergence",
  "title_text": "Ancient cylindrical flows with fast or slow convergence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/czk56c8a2nz5d",
  "venue": "arXiv",
  "versions": []
}