{
  "abstract": "We determine the sharp $L_p$ Brunn--Minkowski range for planar dual quermassintegrals on origin-symmetric convex bodies: $0<q\\leq 2$ for $0\\leq p<1$, and $0<q\\leq4$ for $p=1$. The main new results are the Minkowski inequality for $2<q<4$, proved using a weighted spectral inequality on the projective circle, and parallelogram counterexamples for $0<p<1$ and $q>2$. Together with the known logarithmic and endpoint results, we obtain the complete equality classification: only positive dilates occur, except at $(p,q)=(0,2)$, where parallelograms with corresponding sides parallel also give equality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09636",
  "author_total": 1,
  "authors": [
    {
      "name": "Jiangyan Tao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d45yrh77pj6dt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09636",
  "fulltext_url": null,
  "id": "d45yrh77pj6dt",
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  "landing_url": "https://arxiv.org/abs/2610.09636",
  "language": null,
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  "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.FA"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7220913542",
  "pdf_url": "https://arxiv.org/pdf/2610.09636",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d45yrh77pj6dt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09636",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09636"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the $L_p$ Brunn--Minkowski inequality for planar dual quermassintegrals",
  "title_text": "On the L_p Brunn--Minkowski inequality for planar dual quermassintegrals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/d45yrh77pj6dt",
  "venue": "arXiv",
  "versions": []
}