{
  "id": "2305.09622",
  "version": "v1",
  "published": "2023-05-16T17:20:19.000Z",
  "updated": "2023-05-16T17:20:19.000Z",
  "title": "Prescribing nearly constant curvatures on balls",
  "authors": [
    "Luca Battaglia",
    "Sergio Cruz Blázquez",
    "Angela Pistoia"
  ],
  "comment": "31 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "In this paper we address two boundary cases of the classical Kazdan-Warner problem. More precisely, we consider the problem of prescribing the Gaussian and boundary geodesic curvature on a disk of R^2, and the scalar and mean curvature on a ball in higher dimensions, via a conformal change of the metric. We deal with the case of negative interior curvature and positive boundary curvature. Using a Ljapunov-Schmidt procedure, we obtain new existence results when the prescribed functions are close to constants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-16T17:20:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J25",
      "58J32"
    ],
    "keywords": [
      "constant curvatures",
      "prescribing",
      "boundary geodesic curvature",
      "classical kazdan-warner problem",
      "positive boundary curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}