{
  "abstract": "We study the projection outer volume ratio ${\\rm povr}_k(K)$ introduced by D. Galicer, A.E. Litvak, M. Merzbacher, and D. Pinasco. When $k\\leq n/2$, we provide sharp bounds in the general case, namely \\[ {\\rm povr}_k(K)\\leq C \\max\\Big\\{1, \\sqrt{\\frac{k}{\\ln(2n/k)}}\\Big\\}, \\] where the maximal order is obtained for $K=B_1^n$. Moreover, in the important particular case $K=B_2^n$ we show that ${\\rm povr}_k(B_2^n)$ is bounded by an absolute constant whenever $k\\leq n/2$ and \\[ {\\rm povr}_k(B_2^n)\\leq C\\sqrt{\\frac{n}{n-k}}\\, \\ln\\left(1+\\frac{n}{n-k}\\right) \\] for $k>n/2$. The latter bound is sharp up to a logarithmic term.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09562",
  "author_total": 1,
  "authors": [
    {
      "name": "A. E. Litvak"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/58pdz4nkp2vv1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09562",
  "fulltext_url": null,
  "id": "58pdz4nkp2vv1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09562",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7221038214",
  "pdf_url": "https://arxiv.org/pdf/2610.09562",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/58pdz4nkp2vv1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09562",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09562"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A remark on projection outer volume ratio",
  "title_text": "A remark on projection outer volume ratio",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/58pdz4nkp2vv1",
  "venue": "arXiv",
  "versions": []
}