{
  "id": "math/9912202",
  "version": "v1",
  "published": "1999-12-26T21:26:56.000Z",
  "updated": "1999-12-26T21:26:56.000Z",
  "title": "Negative results for Nikodym maximal functions and related oscillatory integrals in curved space",
  "authors": [
    "William Minicozzi II",
    "Christopher D. Sogge"
  ],
  "journal": "Mathematics Research Letters 4 (1997), 221-237",
  "categories": [
    "math.CA"
  ],
  "abstract": "We expand on counterxamples of Bourgain showing how Nikodym maximal estimates and oscillatory integral estimates can break down in the non-Euclidean case. Our examples show the role that the non-existence of totally geodesic submanifolds can play in these problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-12-26T21:26:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nikodym maximal functions",
      "related oscillatory integrals",
      "negative results",
      "curved space",
      "nikodym maximal estimates"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....12202M"
    }
  }
}