{
  "id": "1208.1808",
  "version": "v3",
  "published": "2012-08-09T03:16:15.000Z",
  "updated": "2018-12-04T16:42:58.000Z",
  "title": "The heat kernel on an asymptotically conic manifold",
  "authors": [
    "David A. Sher"
  ],
  "comment": "35 pages, 10 figures. Version 3: a result of Cheng-Li-Yau was mis-stated in the introduction, requiring minor changes in the proof of Theorem 2 on page 14, but all results still hold",
  "journal": "Anal. PDE 6 (2013) 1755-1791",
  "doi": "10.2140/apde.2013.6.1755",
  "categories": [
    "math.AP",
    "math.SP"
  ],
  "abstract": "In this paper, we investigate the long-time structure of the heat kernel on a Riemannian manifold M which is asymptotically conic near infinity. Using geometric microlocal analysis and building on results of Guillarmou and Hassell on the low-energy resolvent, we give a complete description of the asymptotic structure of the heat kernel in all spatial and temporal regimes. We apply this structure to define and investigate a renormalized zeta function and determinant of the Laplacian on M.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-01T02:49:22.000Z",
      "comment": "35 pages, 10 figures. Version 2: condition c) in Thm. 8 correctly stated, proofs of Prop. 11 and 12 simplified, other minor changes",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2018-12-04T16:42:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J05",
      "58J35",
      "58J52"
    ],
    "keywords": [
      "heat kernel",
      "asymptotically conic manifold",
      "geometric microlocal analysis",
      "long-time structure",
      "low-energy resolvent"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.1808S"
    }
  }
}