{
  "id": "2107.00512",
  "version": "v1",
  "published": "2021-07-01T14:57:51.000Z",
  "updated": "2021-07-01T14:57:51.000Z",
  "title": "Anisotropic symmetrization and Sobolev inequalities on Finsler manifolds with nonnegative Ricci curvature",
  "authors": [
    "Alexandru Kristály",
    "Ágnes Mester",
    "Ildikó I. Mezei"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "By using a sharp isoperimetric inequality and an anisotropic symmetrization argument, we establish Morrey-Sobolev and Hardy-Sobolev inequalities on $n$-dimensional Finsler manifolds having nonnegative $n$-Ricci curvature; in some cases we also discuss the sharpness of these functional inequalities. As applications, by using variational arguments, we guarantee the existence/multiplicity of solutions for certain eigenvalue problems and elliptic PDEs involving the Finsler-Laplace operator. Our results are also new in the Riemannian setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-01T14:57:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonnegative ricci curvature",
      "sharp isoperimetric inequality",
      "dimensional finsler manifolds",
      "anisotropic symmetrization argument",
      "hardy-sobolev inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}