{
  "abstract": "In \\cite {ChenFengLiXiXu2026}, a reverse projection inequality for general convex bodies was established in three dimensions. In this paper, we completely characterize the equality cases of this inequality. We further show that the reverse projection inequality fails in every dimension $n\\geq9$. The counterexamples are constructed as full-dimensional polytopes with at most $n+2$ facets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13953",
  "author_total": 4,
  "authors": [
    {
      "name": "Yibin Feng"
    },
    {
      "name": "Shengnan Hu"
    },
    {
      "name": "Weiru Liu"
    },
    {
      "name": "Lei Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5ysaaz3rqh40k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13953",
  "fulltext_url": null,
  "id": "5ysaaz3rqh40k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13953",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7221756326",
  "pdf_url": "https://arxiv.org/pdf/2610.13953",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5ysaaz3rqh40k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.13953",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13953"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On the Reverse Projection Inequality",
  "title_text": "On the Reverse Projection Inequality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/5ysaaz3rqh40k",
  "venue": "arXiv",
  "versions": []
}