{
  "id": "math/0210084",
  "version": "v2",
  "published": "2002-10-07T19:08:13.000Z",
  "updated": "2002-12-13T22:28:37.000Z",
  "title": "A sharp bilinear restriction estimate for paraboloids",
  "authors": [
    "Terence Tao"
  ],
  "comment": "21 pages, no figures, to appear, GAFA. More explanation added and some minor typos removed",
  "categories": [
    "math.CA"
  ],
  "abstract": "Recently Wolff obtained a sharp $L^2$ bilinear restriction theorem for bounded subsets of the cone in general dimension. Here we adapt the argument of Wolff to also handle subsets of ``elliptic surfaces'' such as paraboloids and spheres. Except for an endpoint, this answers a conjecture of Machedon and Klainerman, and also improves upon the known restriction theory for the paraboloid and sphere.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-12-13T22:28:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B15",
      "35Q55"
    ],
    "keywords": [
      "sharp bilinear restriction estimate",
      "paraboloid",
      "bilinear restriction theorem",
      "restriction theory",
      "elliptic surfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10084T"
    }
  }
}