{
  "abstract": "We prove that Lagrangian mean curvature flow starting from a closed, embedded, cohomogeneity-one Lagrangian in a closed, positive Kähler--Einstein manifold exists for all time, remains embedded, and converges smoothly and graphically to a minimal Lagrangian, under natural exactness and regularity assumptions. We also study the generalised Lagrangian mean curvature flow of Behrndt in Kähler manifolds which are almost-Einstein in the sense that the Ricci form satisfies $ρ= Cω+ ndd^cf$, and which satisfy $C>0$. With analogous assumptions on the flow, we obtain subconvergence to an $f$-minimal Lagrangian submanifold, with an upgrade to smooth graphical convergence in the case that $(M,g,f)$ is analytic. The proof proceeds by first reducing the flow to a weighted curve shortening flow on a compact two-dimensional orbifold. We then establish both a Grayson-type description of finite-time singularities and a long-time subconvergence theorem for weighted curve shortening flow in the orbifold setting. Finally, we use a Łojasiewicz--Simon inequality argument to upgrade to smooth convergence of the full flow.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23627",
  "author_total": 3,
  "authors": [
    {
      "name": "Naotoshi Fujihara"
    },
    {
      "name": "Toru Kajigaya"
    },
    {
      "name": "Albert Wood"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/949b93w9trasv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23627",
  "fulltext_url": null,
  "id": "949b93w9trasv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23627",
  "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": "W7213997380",
  "pdf_url": "https://arxiv.org/pdf/2609.23627",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/949b93w9trasv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23627",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23627"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Convergence of cohomogeneity-one Lagrangian mean curvature flow in positive Kähler-Einstein manifolds",
  "title_text": "Convergence of cohomogeneity-one Lagrangian mean curvature flow in positive Kähler-Einstein manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/949b93w9trasv",
  "venue": "arXiv",
  "versions": []
}