{
  "id": "1709.09506",
  "version": "v1",
  "published": "2017-09-27T13:37:06.000Z",
  "updated": "2017-09-27T13:37:06.000Z",
  "title": "Lower bounds for the first eigenvalue of the magnetic Laplacian",
  "authors": [
    "Bruno Colbois",
    "Alessandro Savo"
  ],
  "comment": "Replaces in part arXiv:1611.01930",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We consider a Riemannian cylinder endowed with a closed potential 1-form A and study the magnetic Laplacian with magnetic Neumann boundary conditions associated with those data. We establish a sharp lower bound for the first eigenvalue and show that the equality characterizes the situation where the metric is a product. We then look at the case of a planar domain bounded by two closed curves and obtain an explicit lower bound in terms of the geometry of the domain. We finally discuss sharpness of this last estimate.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-27T13:37:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J50",
      "35P15"
    ],
    "keywords": [
      "magnetic laplacian",
      "first eigenvalue",
      "magnetic neumann boundary conditions",
      "explicit lower bound",
      "sharp lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}