{
  "abstract": "In this paper, we establish a homological existence criterion for the discrete $L_p$ Minkowski problem for all $p<0$, where $p=-n$ corresponds to the celebrated centro-affine case. For discrete measures with antipodal support, we obtain a complete existence characterization for arbitrary positive masses. In the even case, a solution can be chosen origin-symmetric.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01429",
  "author_total": 1,
  "authors": [
    {
      "name": "Junjie Shan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3q7e2emsqwf9p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01429",
  "fulltext_url": null,
  "id": "3q7e2emsqwf9p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01429",
  "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.CA"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7206150723",
  "pdf_url": "https://arxiv.org/pdf/2609.01429",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3q7e2emsqwf9p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.01429",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01429"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Discrete $L_p$ Minkowski Problem for Negative $p$",
  "title_text": "The Discrete L_p Minkowski Problem for Negative p",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/3q7e2emsqwf9p",
  "venue": "arXiv",
  "versions": []
}