{
  "abstract": "We study complete translating solitons for the mean curvature flow in arbitrary codimension under quadratic pinching of the second fundamental form. We prove a codimension reduction theorem at the Andrews-Baker threshold: if a complete $n$-dimensional connected translator isometrically immersed in $(\\mathbb{R}^{n+p},\\langle\\cdot,\\cdot\\rangle)$ satisfies \\[ |B|^2\\leq \\left(\\frac{4}{3n}-\\varepsilon_{0}\\right)|H|^2 \\] for some $\\varepsilon_{0}>0$, then either it is an affine $n$-plane or $|H|>0$ everywhere and the translator is contained in an $(n+1)$-dimensional affine subspace. In particular, this improves in low dimensions the pinching range previously obtained from codimension reduction results for ancient mean curvature flows. Our proof is purely elliptic: viewing translators as weighted minimal submanifolds, we combine Simons-type identities for the drift Laplacian with refined gradient estimates and an Omori-Yau maximum principle. As a consequence, under the stronger pinching condition \\[ |B|^2\\leq (c_n-\\varepsilon_{0})|H|^2,\\qquad c_n=\\min\\left\\{\\frac{4}{3n},\\frac{1}{n-2}\\right\\} \\] for $n\\geq3$, with $c_n=2/3$ when $n=2$, we obtain a rigidity theorem: the translator is either an affine plane or a bowl soliton contained in an $(n+1)$-dimensional affine subspace. No entropy assumption is required.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01713",
  "author_total": 3,
  "authors": [
    {
      "name": "Debora Impera"
    },
    {
      "name": "Michele Rimoldi"
    },
    {
      "name": "Francesco Ruatta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f40f8szyw5a9h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01713",
  "fulltext_url": null,
  "id": "f40f8szyw5a9h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01713",
  "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": "W7215922720",
  "pdf_url": "https://arxiv.org/pdf/2610.01713",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f40f8szyw5a9h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01713",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01713"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Classification of quadratically pinched translators in higher codimension",
  "title_text": "Classification of quadratically pinched translators in higher codimension",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/f40f8szyw5a9h",
  "venue": "arXiv",
  "versions": []
}