{
  "id": "2407.18776",
  "version": "v1",
  "published": "2024-07-26T14:34:42.000Z",
  "updated": "2024-07-26T14:34:42.000Z",
  "title": "Prescribing almost constant curvatures on manifolds with boundary",
  "authors": [
    "Luca Battaglia",
    "Yixing Pu"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "In this paper, we investigate a boundary case of the classical prescribed curvature problem. We focus on prescribing the scalar curvature function K and the boundary mean curvature H on the standard ball. Our analysis extendes previous studies by considering the scenario where the curvatures K and H are close to constants. Using a perturbative approach and leveraging the ansatz introduced by Han and Li, we establish new existence results for the conformal metric when the prescribed curvatures are near constants",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-26T14:34:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "constant curvatures",
      "boundary mean curvature",
      "scalar curvature function",
      "prescribing",
      "classical prescribed curvature problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}