{
  "id": "1407.1916",
  "version": "v3",
  "published": "2014-07-08T00:42:27.000Z",
  "updated": "2015-02-02T22:43:53.000Z",
  "title": "A restriction estimate using polynomial partitioning",
  "authors": [
    "Larry Guth"
  ],
  "comment": "42 pages. Minor revisions. Accepted for publication in JAMS",
  "categories": [
    "math.CA"
  ],
  "abstract": "If $S$ is a smooth compact surface in $\\mathbb{R}^3$ with strictly positive second fundamental form, and $E_S$ is the corresponding extension operator, then we prove that for all $p > 3.25$, $\\| E_S f\\|_{L^p(\\mathbb{R}^3)} \\le C(p,S) \\| f \\|_{L^\\infty(S)}$. The proof uses polynomial partitioning arguments from incidence geometry.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-04T21:19:22.000Z",
      "comment": "42 pages. Reference updated",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-02-02T22:43:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "restriction estimate",
      "strictly positive second fundamental form",
      "smooth compact surface",
      "incidence geometry",
      "polynomial partitioning arguments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.1916G"
    }
  }
}