{
  "abstract": "We establish the stability of the optimal non-endpoint Fourier restriction range under smooth flat perturbations of curved-root surfaces in $\\mathbb R^3$. Specifically, we consider graphs of $$ϕ(x_1,x_2)=(x_2-x_1^m)^n+R(x_1,x_2),$$ where $m,n\\ge2$ are integers and $R$ is smooth and flat at the origin. On a sufficiently small neighborhood depending on the perturbation, we prove the local $L^p(\\mathbb R^3)\\to L^2(S,dσ)$ restriction estimate for $1\\le p<p_c$, where $$p_c=\\frac{q_c}{q_c-1}, \\qquad q_c=\\max\\left\\{2+\\frac{2mn}{m+1},2n\\right\\}.$$ If the nonnegative localizing density is positive at the origin, an adapted-box example shows that the estimate fails for $p>p_c$. Thus arbitrary smooth flat perturbations preserve the optimal restriction range away from the critical endpoint. For $n\\ge3$, the main local estimate combines planar curve decoupling with a one-dimensional finite-type extension estimate, whose principal scale factors cancel exactly. For $n=2$, we prove a uniform $C^4$ perturbation estimate using a weighted convolution bound and an anisotropic Whitney decomposition. Anisotropic rescaling and summation complete the proof.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31389",
  "author_total": 3,
  "authors": [
    {
      "name": "Wenjuan Li"
    },
    {
      "name": "Hongqiang Wang"
    },
    {
      "name": "Huiju Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5gg213ypjkpz5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31389",
  "fulltext_url": null,
  "id": "5gg213ypjkpz5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31389",
  "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.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7223373913",
  "pdf_url": "https://arxiv.org/pdf/2610.31389",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5gg213ypjkpz5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31389",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31389"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Stability of Fourier Restriction for a Class of Finite Type Surfaces in $\\mathbb R^3$",
  "title_text": "Stability of Fourier Restriction for a Class of Finite Type Surfaces in ℝ^3",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/5gg213ypjkpz5",
  "venue": "arXiv",
  "versions": []
}