{
  "id": "2209.10713",
  "version": "v1",
  "published": "2022-09-22T00:27:56.000Z",
  "updated": "2022-09-22T00:27:56.000Z",
  "title": "Lower bounds for the first eigenvalue of $p$-Laplacian on Kähler manifolds",
  "authors": [
    "Kui Wang",
    "Shaoheng Zhang"
  ],
  "comment": "All comments are welcome!",
  "categories": [
    "math.DG",
    "math.AP",
    "math.SP"
  ],
  "abstract": "We study the eigenvalue problem for the $p$-Laplacian on K\\\"ahler manifolds. Our first result is a lower bound for the first nonzero eigenvalue of the $p$-Laplacian on compact K\\\"ahler manifolds in terms of dimension, diameter, and lower bounds of holomorphic sectional curvature and orthogonal Ricci curvature for $p\\in (1, 2]$. Our second result is a sharp lower bound for the first Dirichlet eigenvalue of the $p$-Laplacian on compact K\\\"ahler manifolds with smooth boundary for $p\\in (1, \\infty)$. Our results generalize corresponding results for the Laplace eigenvalues on K\\\"ahler manifolds proved in [14].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-22T00:27:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P15",
      "53C55"
    ],
    "keywords": [
      "kähler manifolds",
      "first eigenvalue",
      "holomorphic sectional curvature",
      "first dirichlet eigenvalue",
      "sharp lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}