{
  "abstract": "Let \\(A,B\\subset\\R^2\\) be nonempty Borel sets. We prove that \\[ \\dimH(gA-B)\\ge\\min\\{\\dimH A+\\dimH B,2\\} \\] for almost all \\(g\\in\\mathrm O(2)\\). This bound is sharp in general, and the proof gives a corresponding statement for the lower Hausdorff dimension of convolutions of Frostman measures. We also prove that \\(\\LL^2(gA-B)>0\\) for almost all \\(g\\) if both dimensions exceed \\((\\sqrt{13}-1)/2\\). The second result follows from an angular decomposition, refined decoupling and a two-ends Furstenberg estimate. Some applications on intersection patterns are also addressed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16114",
  "author_total": 3,
  "authors": [
    {
      "name": "Thang Pham"
    },
    {
      "name": "Chun-Yen Shen"
    },
    {
      "name": "Dung The Tran"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bhyzc8k9w0mdf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16114",
  "fulltext_url": null,
  "id": "bhyzc8k9w0mdf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16114",
  "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.CO"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7221833282",
  "pdf_url": "https://arxiv.org/pdf/2610.16114",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bhyzc8k9w0mdf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16114",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16114"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On Mattila's intersection problem in the plane: sharp dimension and positive measure of rotated difference sets",
  "title_text": "On Mattila's intersection problem in the plane: sharp dimension and positive measure of rotated difference sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/bhyzc8k9w0mdf",
  "venue": "arXiv",
  "versions": []
}