{
  "id": "math/0404418",
  "version": "v5",
  "published": "2004-04-22T17:58:42.000Z",
  "updated": "2005-01-04T02:46:17.000Z",
  "title": "Estimates on the Lower Bound of the First Gap",
  "authors": [
    "Jun Ling"
  ],
  "comment": "enhanced results, 26 pages",
  "categories": [
    "math.DG",
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We give a new lower bound for the first gap $\\lambda_2 - \\lambda_1$ of the Dirichlet eigenvalues of the Schr{\\\"o}dinger operator on a bounded convex domain $\\Omega$ in R$^n$ or S$^n$ and greatly sharpens the previous estimates. The new bound is explicit and computable.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2005-01-04T02:46:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J10",
      "35P15",
      "53C21"
    ],
    "keywords": [
      "lower bound",
      "first gap",
      "dirichlet eigenvalues",
      "bounded convex domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4418L"
    }
  }
}