{
  "id": "2404.01962",
  "version": "v1",
  "published": "2024-04-02T13:55:39.000Z",
  "updated": "2024-04-02T13:55:39.000Z",
  "title": "Existence of solutions to the generalized dual Minkowski problem",
  "authors": [
    "Mingyang Li",
    "Yannan Liu",
    "Jian Lu"
  ],
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "Given a real number $q$ and a star body in the $n$-dimensional Euclidean space, the generalized dual curvature measure of a convex body was introduced by Lutwak-Yang-Zhang [43]. The corresponding generalized dual Minkowski problem is studied in this paper. By using variational methods, we solve the generalized dual Minkowski problem for $q<0$, and the even generalized dual Minkowski problem for $0\\leq q\\leq1$. We also obtain a sufficient condition for the existence of solutions to the even generalized dual Minkowski problem for $1<q<n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-02T13:55:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A20",
      "35J96"
    ],
    "keywords": [
      "dimensional euclidean space",
      "corresponding generalized dual minkowski problem",
      "generalized dual curvature measure",
      "star body",
      "sufficient condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}