{
  "id": "1409.1286",
  "version": "v1",
  "published": "2014-09-03T23:43:35.000Z",
  "updated": "2014-09-03T23:43:35.000Z",
  "title": "Refined and microlocal Kakeya-Nikodym bounds for eigenfunctions in two dimensions",
  "authors": [
    "Matthew D. Blair",
    "Christopher D. Sogge"
  ],
  "comment": "17 pages, 2 figures",
  "categories": [
    "math.AP",
    "math.CA",
    "math.DG"
  ],
  "abstract": "We obtain some improved essentially sharp Kakeya-Nikodym estimates for eigenfunctions in two-dimensions. We obtain these by proving stronger related microlocal estimates involving a natural decomposition of phase space that is adapted to the geodesic flow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-03T23:43:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "microlocal kakeya-nikodym bounds",
      "eigenfunctions",
      "dimensions",
      "essentially sharp kakeya-nikodym estimates",
      "proving stronger related microlocal estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.1286B"
    }
  }
}