{
  "id": "math/9810107",
  "version": "v1",
  "published": "1998-10-17T02:11:40.000Z",
  "updated": "1998-10-17T02:11:40.000Z",
  "title": "Analysis and Geometry of Boundary-Manifolds of Bounded Geometry",
  "authors": [
    "Thomas Schick"
  ],
  "comment": "AMS-Latex2e, 41 pages",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "In this paper, we investigate analytical and geometric properties of certain non-compact boundary-manifolds, namely manifolds of bounded geometry. One result are strong Bochner type vanishing results for the L^2-cohomology of these manifolds: if e.g. a manifold admits a metric of bounded geometry which outside a compact set has nonnegative Ricci curvature and nonnegative mean curvature (of the boundary) then its first relative L^2-cohomology vanishes (this in particular answers a question of Roe). We prove the Hodge-de Rham-theorem for L^2-cohomology of oriented boundary-manifolds of bounded geometry. The technical basis is the study of (uniformly elliptic) boundary value problems on these manifolds, applied to the Laplacian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-10-17T02:11:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "58G20",
      "57R19"
    ],
    "keywords": [
      "bounded geometry",
      "strong bochner type vanishing results",
      "boundary value problems",
      "geometric properties",
      "hodge-de rham-theorem"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....10107S"
    }
  }
}