{
  "id": "2304.06561",
  "version": "v1",
  "published": "2023-04-13T14:14:53.000Z",
  "updated": "2023-04-13T14:14:53.000Z",
  "title": "Nguyen's approach to Sobolev spaces in metric measure spaces with unique tangents",
  "authors": [
    "Camillo Brena",
    "Andrea Pinamonti"
  ],
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "We extend Nguyen's characterization of Sobolev spaces $W^{1,p}$ to the setting of PI-metric measure spaces such that at a.e. point the tangent space (in the Gromov-Hausdorff sense) is unique and Euclidean with a fixed dimension. We also generalize [CLL14] to PI-metric measure spaces such that at a.e. point the tangent space is unique and equal to the Heisenberg group with a fixed homogeneous dimension. The approach is easier and completely different from the one in [Ngu06, Ngu08].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-13T14:14:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sobolev spaces",
      "nguyens approach",
      "unique tangents",
      "pi-metric measure spaces",
      "tangent space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}