{
  "id": "2310.03369",
  "version": "v1",
  "published": "2023-10-05T08:03:08.000Z",
  "updated": "2023-10-05T08:03:08.000Z",
  "title": "The Injectivity Radius of Souls of Alexandrov Spaces",
  "authors": [
    "Elena Mäder-Baumdicker",
    "Jona Seidel"
  ],
  "comment": "Comments are welcome",
  "categories": [
    "math.DG",
    "math.MG"
  ],
  "abstract": "We generalize a sharp lower bound of the injectivity radius in noncompact nonnegatively curved Riemannian manifolds found by \\v{S}arafutdinov to the setting of Alexandrov spaces. The injectivity radius either coincides with that of souls or is not less than $ \\pi K^{-1/2} $, where $ K $ is an upper curvature bound. We give an introduction to the theory of the soul of Alexandrov spaces and compare two injectivity radii.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-05T08:03:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "53C23",
      "53C45"
    ],
    "keywords": [
      "injectivity radius",
      "alexandrov spaces",
      "sharp lower bound",
      "upper curvature bound",
      "noncompact nonnegatively curved riemannian manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}