{
  "id": "2406.11120",
  "version": "v1",
  "published": "2024-06-17T00:43:02.000Z",
  "updated": "2024-06-17T00:43:02.000Z",
  "title": "Neumann cut-offs and essential self-adjointness on complete Riemannian manifolds with boundary",
  "authors": [
    "Davide Bianchi",
    "Batu Güneysu",
    "Alberto G. Setti"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We generalize some fundamental results for noncompact Riemannian manfolds without boundary, that only require completeness and no curvature assumptions, to manifolds with boundary: let $M$ be a smooth Riemannian manifold with boundary $\\partial M$ and let $\\hat{C}^\\infty_c(M)$ denote the space of smooth compactly supported cut-off functions with vanishing normal derivative, Neumann cut-offs. We show, among other things, that under completeness: - $\\hat{C}^\\infty_c(M)$ is dense in $W^{1,p}(\\mathring{M})$ for all $p\\in (1,\\infty)$; this generalizes a classical result by Aubin [2] for $\\partial M=\\emptyset$. - $M$ admits a sequence of first order cut-off functions in $\\hat{C}^\\infty_c(M)$; for $\\partial M=\\emptyset$ this result can be traced back to Gaffney [7]. - the Laplace-Beltrami operator with domain of definition $\\hat{C}^\\infty_c(M)$ is essentially self-adjoint; this is a generalization of a classical result by Strichartz [20] for $\\partial M=\\emptyset$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-17T00:43:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J05",
      "58J50",
      "35J25"
    ],
    "keywords": [
      "complete riemannian manifolds",
      "neumann cut-offs",
      "essential self-adjointness",
      "compactly supported cut-off functions",
      "first order cut-off functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}