{
  "abstract": "It is shown that if $u$ solves the wave equation in $\\mathbb{R}^{4+1}$ with initial data $u(\\cdot,0) = u_0(\\cdot) \\in H^s$ and $\\partial_tu(\\cdot,0) = u_1(\\cdot ) \\in H^{s-1}$, where $0.5 < s \\leq 0.55$, then $u(x,t) \\to u_0(x)$ and $\\partial_tu(x,t) \\to u_1(x)$ pointwise as $t \\to 0$, for all $x$ outside an exceptional set of Hausdorff dimension at most $6-4s$. In a very small range of $s$, this verifies a conjecture of Barceló, Bennett, Carbery, and Rogers. More generally, a partial improvement to the exceptional set bound in $\\mathbb{R}^{n+1}$ is obtained for $n \\geq 4$ and $1/2 < s < n/4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19691",
  "author_total": 3,
  "authors": [
    {
      "name": "Xiumin Du"
    },
    {
      "name": "Terence L. J. Harris"
    },
    {
      "name": "Jianhui Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bm59er1jae8tv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19691",
  "fulltext_url": null,
  "id": "bm59er1jae8tv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19691",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "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.AP"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7213612565",
  "pdf_url": "https://arxiv.org/pdf/2609.19691",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bm59er1jae8tv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19691",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19691"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The divergence set for the wave equation in higher dimensions",
  "title_text": "The divergence set for the wave equation in higher dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/bm59er1jae8tv",
  "venue": "arXiv",
  "versions": []
}