{
  "id": "1208.1809",
  "version": "v2",
  "published": "2012-08-09T03:32:15.000Z",
  "updated": "2013-10-01T01:55:01.000Z",
  "title": "Conic degeneration and the determinant of the Laplacian",
  "authors": [
    "David A. Sher"
  ],
  "comment": "41 pages, 7 figures. Version 2: bug fixed in Theorem 2 statement, other minor changes",
  "categories": [
    "math.AP",
    "math.SP"
  ],
  "abstract": "We investigate the behavior of various spectral invariants, particularly the determinant of the Laplacian, on a family of smooth Riemannian manifolds which undergo conic degeneration; that is, which converge in a particular way to a manifold with a conical singularity. Our main result is an asymptotic formula for the determinant up to terms which vanish as the degeneration parameter goes to zero. The proof proceeds in two parts; we study the fine structure of the heat trace on the degenerating manifolds via a parametrix construction, and then use that fine structure to analyze the zeta function and determinant of the Laplacian.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-01T01:55:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J05",
      "58J52",
      "58J35",
      "58J50"
    ],
    "keywords": [
      "determinant",
      "fine structure",
      "smooth riemannian manifolds",
      "undergo conic degeneration",
      "spectral invariants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.1809S"
    }
  }
}