{
  "abstract": "We study ancient solutions to curve shortening flow on a class of warped product surfaces. For closed embedded ancient solutions whose curves are not null-homotopic, we prove that graphicality at every time is equivalent to a uniform length bound as $t\\to-\\infty$, and that these properties hold whenever the length is $o(\\sqrt{-t})$. Under an additional positivity condition on the linearized height equation, every such solution with bounded length is a family of slices. We derive backward convergence to a limiting circle from the length bound and prove slice rigidity by an $L^2$ estimate for the height perturbation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34274",
  "author_total": 2,
  "authors": [
    {
      "name": "Beomseok Goh"
    },
    {
      "name": "Taehun Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fj10kmrxdkdeb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34274",
  "fulltext_url": null,
  "id": "fj10kmrxdkdeb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34274",
  "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": "W7223819469",
  "pdf_url": "https://arxiv.org/pdf/2610.34274",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fj10kmrxdkdeb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34274",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34274"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Length bounds and rigidity for ancient curve shortening flow on warped product surfaces",
  "title_text": "Length bounds and rigidity for ancient curve shortening flow on warped product surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/fj10kmrxdkdeb",
  "venue": "arXiv",
  "versions": []
}