{
  "abstract": "We present a proof for the $(n-2)$-linear extension estimate for curved surfaces in $\\mathbb{R}^n$, $n\\ge5$, at the local product exponent $2(n-1)/(n-2)^2$, with an arbitrarily small power loss. The hypotheses are transversality of the normals and nondegeneracy of the compressed shape operators on their common two-dimensional orthogonal complement. The argument combines polynomial partitioning, a descent through algebraic varieties, localized multilinear restriction, and positive packet-energy estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25907",
  "author_total": 1,
  "authors": [
    {
      "name": "Faruk Temur"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eyhgcp4f4bqsn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25907",
  "fulltext_url": null,
  "id": "eyhgcp4f4bqsn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25907",
  "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",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7223064434",
  "pdf_url": "https://arxiv.org/pdf/2610.25907",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eyhgcp4f4bqsn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25907",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25907"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The $(n-2)$-linear restriction estimate in $\\mathbb R^n$",
  "title_text": "The (n−2)-linear restriction estimate in ℝ^n",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/eyhgcp4f4bqsn",
  "venue": "arXiv",
  "versions": []
}