{
  "id": "2205.13372",
  "version": "v1",
  "published": "2022-05-26T13:53:30.000Z",
  "updated": "2022-05-26T13:53:30.000Z",
  "title": "Reverse Faber-Krahn inequality for the $p$-Laplacian in Hyperbolic space",
  "authors": [
    "Mrityunjoy Ghosh",
    "Sheela Verma"
  ],
  "categories": [
    "math.AP",
    "math.DG",
    "math.OC"
  ],
  "abstract": "In this paper, we study the shape optimization problem for the first eigenvalue of the $p$-Laplace operator with the mixed Neumann-Dirichlet boundary conditions on multiply-connected domains in hyperbolic space. Precisely, we establish that among all multiply-connected domains of a given volume and prescribed $(n-1)$-th quermassintegral of the convex Dirichlet boundary (inner boundary), the concentric annular region produces the largest first eigenvalue. We also derive Nagy's type inequality for outer parallel sets of a convex domain in the hyperbolic space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-26T13:53:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58C40",
      "35P15",
      "35P30",
      "49R05"
    ],
    "keywords": [
      "hyperbolic space",
      "reverse faber-krahn inequality",
      "concentric annular region produces",
      "derive nagys type inequality",
      "largest first eigenvalue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}