{
  "id": "2107.08859",
  "version": "v1",
  "published": "2021-07-19T13:22:23.000Z",
  "updated": "2021-07-19T13:22:23.000Z",
  "title": "Noncritical maps on geodesically complete spaces with curvature bounded above",
  "authors": [
    "Tadashi Fujioka"
  ],
  "categories": [
    "math.DG",
    "math.MG"
  ],
  "abstract": "We define and study the regularity of distance maps on geodesically complete spaces with curvature bounded above. We prove that such a regular map is locally a Hurewicz fibration. This regularity can be regarded as a dual concept of Perelman's regularity for distance maps on Alexandrov spaces with curvature bounded below.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-19T13:22:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "53C21",
      "53C23"
    ],
    "keywords": [
      "geodesically complete spaces",
      "noncritical maps",
      "distance maps",
      "perelmans regularity",
      "dual concept"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}