{
  "abstract": "The paper studies the weighted dual Minkowski problem for the weighted $q$th dual curvature measure of convex bodies in $\\mathbb R^n$ first posed by Huang, Lutwak, Yang, and Zhang. Most of the results are in the G-invariant setting, i.e. when the convex bodies are invariant under a closed subgroup $G$ of $O(n)$. They generalize previous results on the existence of solutions to the dual Minkowski problem for origin-symmetric convex bodies. It is proved: (i) a full characterization of the G-invariant weighted dual curvature measure for q\\in(0,1], (ii) a necessary and sufficient condition for the existence of solutions to the G-invariant weighted dual Minkowski problem for q\\in(1,n), (iii) a sufficient condition for the G-invariant weighted dual curvature measure for q>1, and (iv) an extension of Henk-Pollehn's dual curvature measure concentration property.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20047",
  "author_total": 3,
  "authors": [
    {
      "name": "Karoly J. Boroczky"
    },
    {
      "name": "Stephanie Mui"
    },
    {
      "name": "Gaoyong Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dzgsk8tetv9se.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20047",
  "fulltext_url": null,
  "id": "dzgsk8tetv9se",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20047",
  "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.AP"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7213594136",
  "pdf_url": "https://arxiv.org/pdf/2609.20047",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dzgsk8tetv9se.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.20047",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20047"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Weighted Dual Minkowski Problem Under Group Symmetry",
  "title_text": "The Weighted Dual Minkowski Problem Under Group Symmetry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/dzgsk8tetv9se",
  "venue": "arXiv",
  "versions": []
}