{
  "abstract": "In the upper half-space model of the hyperbolic space $\\mathbb{H}^{n+1}$, a translation hypersurface of type I is a graph $x_{n+1}=f_1(x_1)+\\cdots+f_n(x_n)$ and a translation hypersurface of type II is a graph $x_n=f_1(x_1)+\\cdots+f_{n-1}(x_{n-1})+g(x_{n+1})$. We classify the minimal translation hypersurfaces of both types for every $n\\geq 2$. We obtain these results as particular cases of a classification of the singular minimal translation hypersurfaces of $\\mathbb{R}^{n+1}$ for an arbitrary exponent $α\\neq 0$, with respect to a direction orthogonal (type I) or parallel (type II) to the hyperplane over which the hypersurface is a graph. The minimal translation hypersurfaces of type I are exactly the parabolic cylinders over a one-parameter family of arches, which contradicts a nonexistence theorem in the literature. The minimal translation hypersurfaces of type II are the parabolic cylinders, the vertical totally geodesic hyperplanes and, when $n\\geq 3$, the vertical cylinders over the Scherk surface.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10363",
  "author_total": 1,
  "authors": [
    {
      "name": "Ameth Ndiaye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ftma8w05cs3p3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10363",
  "fulltext_url": null,
  "id": "ftma8w05cs3p3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10363",
  "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": "W7220960471",
  "pdf_url": "https://arxiv.org/pdf/2610.10363",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ftma8w05cs3p3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10363",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10363"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Minimal translation hypersurfaces in hyperbolic space",
  "title_text": "Minimal translation hypersurfaces in hyperbolic space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/ftma8w05cs3p3",
  "venue": "arXiv",
  "versions": []
}