{
  "abstract": "Let $Θ\\subset\\mathbb{R}^n$, $n\\geq 1$ be compact with upper Minkowski dimension $β$, and let $γ(x,t,θ)$ be a family of curves which is bi-Lipschitz in the first variable and Lipschitz in the last two. We prove the maximal estimate $$\\left\\|\\sup_{(τ,θ)\\in[0,1)\\timesΘ}\\left|e^{iτΔ}f(γ(\\,\\cdot\\,,τ,θ))\\right|\\right\\|_{L^2(B^n_1)}\\lesssim_s\\|f\\|_{H^s(\\mathbb{R}^n)},$$ for every $s>\\tfrac{n(β+1)}{2(n+1)}$, in the range $0\\leβ\\le n-1$. In the range $n-1<β\\leq n$ we prove the threshold $s>\\min\\big\\lbrace\\fracβ2 + \\frac 1{2(n+1)},\\frac n2\\big\\rbrace$. The proof relies on a fractal $L^2$ estimate of Du--Zhang. We also use the temporal localization of Lee, the locally constant property, and a counting argument allowed by the Lipschitz properties of the curve.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12565",
  "author_total": 1,
  "authors": [
    {
      "name": "Javier Minguillón"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/741dqas7hsejd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12565",
  "fulltext_url": null,
  "id": "741dqas7hsejd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12565",
  "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.AP"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7221525313",
  "pdf_url": "https://arxiv.org/pdf/2610.12565",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/741dqas7hsejd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12565",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12565"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A higher-dimensional Schrödinger maximal estimate along families of bi-Lipschitz curves",
  "title_text": "A higher-dimensional Schrödinger maximal estimate along families of bi-Lipschitz curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/741dqas7hsejd",
  "venue": "arXiv",
  "versions": []
}