{
  "id": "2112.03542",
  "version": "v2",
  "published": "2021-12-07T07:35:08.000Z",
  "updated": "2025-02-11T09:41:50.000Z",
  "title": "Lower bounds for the spectral gap and an extension of the Bonnet-Myers theorem",
  "authors": [
    "Michel Bonnefont",
    "El Maati Ouhabaz"
  ],
  "comment": "Final version, to appear in Potential Analysis",
  "categories": [
    "math.AP",
    "math.FA",
    "math.SP"
  ],
  "abstract": "On a fairly general class of Riemannian manifolds M, we prove lower estimates in terms of the Ricci curvature for the spectral bound (when M has infinite volume) and for the spectral gap (when M has finite volume) for the Laplace-Beltrami operator. As a byproduct of our results we obtain an extension of the Bonnet-Myers theorem on the compactness of the manifold. We also prove lower bounds for the spectral gap for Ornstein-Uhlenbeck type operators on weighted manifolds. As an application we prove lower bounds for the spectral gap of perturbations of some radial measures on R n .",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-02-11T09:41:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral gap",
      "lower bounds",
      "bonnet-myers theorem",
      "ornstein-uhlenbeck type operators",
      "lower estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}