{
  "id": "1010.4579",
  "version": "v2",
  "published": "2010-10-21T20:34:02.000Z",
  "updated": "2010-11-01T14:28:33.000Z",
  "title": "A Remark on Recent Lower Bounds for Nodal Sets",
  "authors": [
    "Dan Mangoubi"
  ],
  "comment": "4 pages; In section 2 an explanation of the basic iteration idea is added; acknowledgments added",
  "journal": "Comm. Partial Differential Equations 36 (2011), no. 12, 2208--2212",
  "doi": "10.1080/03605302.2011.558556",
  "categories": [
    "math.AP",
    "math.DG",
    "math.SP"
  ],
  "abstract": "Recently, Sogge-Zelditch and Colding-Minicozzi gave new power law lower bounds on the size of the nodal sets of eigenfunctions. The purpose of this short note is to point out a third method to obtain a power law lower bound on the volume of the nodal sets. Our method is based on the Donnelly-Fefferman growth bound for eigenfunctions and a growth vs. volume relation we proved in a previous work.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-11-01T14:28:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P20"
    ],
    "keywords": [
      "nodal sets",
      "power law lower bound",
      "donnelly-fefferman growth bound",
      "colding-minicozzi gave",
      "eigenfunctions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.4579M"
    }
  }
}