{
  "id": "math-ph/0207017",
  "version": "v1",
  "published": "2002-07-14T09:22:06.000Z",
  "updated": "2002-07-14T09:22:06.000Z",
  "title": "Periodic Manifolds with Spectral Gaps",
  "authors": [
    "Olaf Post"
  ],
  "comment": "21 pages, 3 eps-figures, LaTeX",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We investigate spectral properties of the Laplace operator on a class of non-compact Riemannian manifolds. For a given number $N$ we construct periodic (i.e. covering) manifolds such that the essential spectrum of the corresponding Laplacian has at least $N$ open gaps. We use two different methods. First, we construct a periodic manifold starting from an infinite number of copies of a compact manifold, connected by small cylinders. In the second construction we begin with a periodic manifold which will be conformally deformed. In both constructions, a decoupling of the different period cells is responsible for the gaps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-07-14T09:22:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic manifold",
      "spectral gaps",
      "non-compact riemannian manifolds",
      "construct periodic",
      "spectral properties"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/S0022-0396(02)00006-2",
      "journal": "Journal of Differential Equations",
      "year": 2003,
      "volume": 187,
      "number": 1,
      "pages": 23
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003JDE...187...23P"
    }
  }
}