{
  "abstract": "This short note gives a very short unified proof of both Dar's conjecture and the log-Brunn--Minkowski inequality in the plane. A planar $L_p$-Brunn-Minkowski inequality for $p\\in [-\\infty,0]$ is established and gives the two key inequalities at $p=0$ and $p=-\\infty$. Motivated by this new proof, the author proposes a related conjecture in $\\tr^3$, to attack the two conjectures in higher dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08495",
  "author_total": 1,
  "authors": [
    {
      "name": "Dongmeng Xi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d46dhkmcje8dm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08495",
  "fulltext_url": null,
  "id": "d46dhkmcje8dm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08495",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7212044020",
  "pdf_url": "https://arxiv.org/pdf/2609.08495",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d46dhkmcje8dm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08495",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08495"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A very short unified proof of Dar's conjecture and Log-Brunn--Minkowski in the plane",
  "title_text": "A very short unified proof of Dar's conjecture and Log-Brunn--Minkowski in the plane",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/d46dhkmcje8dm",
  "venue": "arXiv",
  "versions": []
}