{
  "abstract": "We provide an alternative and independent proof of the analogue of the Gage-Hamilton-Grayson Theorem for embedded free boundary curve shortening flows in a convex planar domain established by Langford-Zhu. Our proof is based on blowup arguments introduced by B. White in his work on mean-convex mean curvature flow.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09557",
  "author_total": 2,
  "authors": [
    {
      "name": "Yueheng Bao"
    },
    {
      "name": "Lorenzo Sarnataro"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/80zdjg58kg8zw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09557",
  "fulltext_url": null,
  "id": "80zdjg58kg8zw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09557",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
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      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
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  "openalex": "W7221052574",
  "pdf_url": "https://arxiv.org/pdf/2610.09557",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/80zdjg58kg8zw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.09557",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09557"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On the Gage-Hamilton-Grayson Theorem for free boundary curves",
  "title_text": "On the Gage-Hamilton-Grayson Theorem for free boundary curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/80zdjg58kg8zw",
  "venue": "arXiv",
  "versions": []
}