{
  "abstract": "Let $n\\ge3$ and $D_t=\\operatorname{diag}(t^{g_1},\\ldots,t^{g_n})$ be a positive diagonal dilation family. We study connected embedded Euclidean hypersurfaces whose diagonal images are minimal. The level-set minimality operator splits into coefficients indexed by the pair sums $g_i+g_j$. Under pair-sum nonresonance, minimality at only $\\binom n2$ distinct dilation parameters forces all pair coefficients to vanish. A dimension-reduction argument then shows, without any hypothesis on the coordinate components of the normal, that the second fundamental form vanishes identically. This yields an affine characterization. Repeated-weight helicoidal examples in every dimension and a resonant quadratic cone show that curvature cancellation can survive in genuinely nonuniform families. An application gives a finite-output-level rigidity criterion and an explicit representation for weighted-homogeneous production functions with minimal isoquants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00668",
  "author_total": 3,
  "authors": [
    {
      "name": "Jongha Lee"
    },
    {
      "name": "Suhwan Lee"
    },
    {
      "name": "Jae Won Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fj4dms9z28w27.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00668",
  "fulltext_url": null,
  "id": "fj4dms9z28w27",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00668",
  "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.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7206188794",
  "pdf_url": "https://arxiv.org/pdf/2609.00668",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fj4dms9z28w27.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00668",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00668"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Rigidity of Euclidean Minimal Hypersurfaces under Nonuniform Diagonal Dilations",
  "title_text": "Rigidity of Euclidean Minimal Hypersurfaces under Nonuniform Diagonal Dilations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/fj4dms9z28w27",
  "venue": "arXiv",
  "versions": []
}