{
  "id": "math-ph/0410022",
  "version": "v1",
  "published": "2004-10-07T07:07:10.000Z",
  "updated": "2004-10-07T07:07:10.000Z",
  "title": "Elliptic operators on planar graphs: Unique continuation for eigenfunctions and nonpositive curvature",
  "authors": [
    "S. Klassert",
    "D. Lenz",
    "N. Peyerimhoff",
    "P. Stollmann"
  ],
  "categories": [
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "This paper is concerned with elliptic operators on plane tessellations. We show that such an operator does not admit a compactly supported eigenfunction, if the combinatorial curvature of the tessellation is nonpositive. Furthermore, we show that the only geometrically finite, repetitive plane tessellations with nonpositive curvature are the regular $(3,6), (4,4)$ and $(6,3)$ tilings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-10-07T07:07:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "35J10",
      "82B44"
    ],
    "keywords": [
      "elliptic operators",
      "nonpositive curvature",
      "planar graphs",
      "unique continuation",
      "repetitive plane tessellations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.ph..10022K"
    }
  }
}