{
  "id": "1408.2624",
  "version": "v2",
  "published": "2014-08-12T05:41:53.000Z",
  "updated": "2014-08-23T19:31:08.000Z",
  "title": "An integral formula in Kahler geometry with applications",
  "authors": [
    "Xiaodong Wang"
  ],
  "comment": "revised",
  "categories": [
    "math.DG",
    "math.CV"
  ],
  "abstract": "We establish an integral formula on a smooth, precompact domain in a Kahler manifold. We apply this formula to study holomorphic extension of CR functions. Using this formula we prove an isoperimetric inequality in terms of a positive lower bound for the Hermitian curvature of the boundary. Combining with a Minkowski type formula on the complex hyperbolic space we prove that any closed, embedded hypersurface of constant mean curvature must be a geodesic sphere, provided the hypersurface is Hopf. A similar result is established on the complex projective space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-12T05:41:53.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-08-23T19:31:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integral formula",
      "kahler geometry",
      "applications",
      "constant mean curvature",
      "minkowski type formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.2624W"
    }
  }
}