{
  "id": "1111.5323",
  "version": "v1",
  "published": "2011-11-22T20:52:50.000Z",
  "updated": "2011-11-22T20:52:50.000Z",
  "title": "A Lichnerowicz estimate for the first eigenvalue of convex domains in Kähler manifolds",
  "authors": [
    "Boris Kolev",
    "Vincent Guedj",
    "Nader Yeganefar"
  ],
  "comment": "9 pages",
  "journal": "Analysis \\& PDE 6, 5 (2013) 1001-1012",
  "doi": "10.2140/apde.2013.6.1001",
  "categories": [
    "math.DG",
    "math.CV"
  ],
  "abstract": "In this article, we prove a Lichnerowicz estimate for a compact convex domain of a K\\\"ahler manifold whose Ricci curvature satisfies $\\Ric \\ge k$ for some constant $k>0$. When equality is achieved, the boundary of the domain is totally geodesic and there exists a nontrivial holomorphic vector field. We show that a ball of sufficiently large radius in complex projective space provides an example of a strongly pseudoconvex domain which is not convex, and for which the Lichnerowicz estimate fails.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-22T20:52:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first eigenvalue",
      "kähler manifolds",
      "nontrivial holomorphic vector field",
      "compact convex domain",
      "ricci curvature satisfies"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.5323K"
    }
  }
}