{
  "id": "2311.09451",
  "version": "v1",
  "published": "2023-11-15T23:41:07.000Z",
  "updated": "2023-11-15T23:41:07.000Z",
  "title": "Shadow geometry at singular points of CAT(k) spaces",
  "authors": [
    "Jonathan C. Mattingly",
    "Ezra Miller",
    "Do Tran"
  ],
  "comment": "19 pages, 8 figures. This is the first in a four-part series leading to central limit theorems on stratified spaces",
  "categories": [
    "math.MG"
  ],
  "abstract": "In any CAT(k) space M, the \"shadow\" of a tangent vector Z at a point p is the set vectors that form an angle of \\pi or more with Z. Taking logarithm maps at points approaching p along a fixed geodesic ray from p with tangent Z collapses the shadow to a single ray while leaving isometrically intact every convex cone that avoids the shadow of Z.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-15T23:41:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C23",
      "49J52",
      "58K30",
      "53C80",
      "60F05",
      "60D05",
      "62R20",
      "62R07",
      "92B10"
    ],
    "keywords": [
      "singular points",
      "shadow geometry",
      "tangent vector",
      "logarithm maps",
      "convex cone"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}