{
  "id": "1109.1995",
  "version": "v2",
  "published": "2011-09-09T13:05:28.000Z",
  "updated": "2012-12-06T08:46:15.000Z",
  "title": "Counting function of the embedded eigenvalues for some manifold with cusps, and magnetic Laplacian",
  "authors": [
    "Abderemane Morame",
    "Francoise Truc"
  ],
  "journal": "Mathematical Review Letters 19, (2) (2012) pp 417-429",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a non compact, complete manifold {\\bf{M}} of finite area with cuspidal ends. The generic cusp is isomorphic to ${\\bf{X}}\\times ]1,+\\infty [$ with metric $ds^2=(h+dy^2)/y^{2\\delta}.$ {\\bf{X}} is a compact manifold with nonzero first Betti number equipped with the metric $h.$ For a one-form $A$ on {\\bf{M}} such that in each cusp $A$ is a non exact one-form on the boundary at infinity, we prove that the magnetic Laplacian $-\\Delta_A=(id+A)^\\star (id+A)$ satisfies the Weyl asymptotic formula with sharp remainder. We deduce an upper bound for the counting function of the embedded eigenvalues of the Laplace-Beltrami operator $-\\Delta =-\\Delta_0.$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-12-06T08:46:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "magnetic laplacian",
      "counting function",
      "embedded eigenvalues",
      "nonzero first betti number",
      "non exact one-form"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.1995M"
    }
  }
}