{
  "id": "1105.3150",
  "version": "v3",
  "published": "2011-05-16T17:04:42.000Z",
  "updated": "2011-08-29T15:06:24.000Z",
  "title": "The space of Constant Mean Curvature surfaces in compact Riemannian Manifolds",
  "authors": [
    "Jose M. Espinar"
  ],
  "comment": "The paper have been withdrawn since the cornerstone area estimate (Theorem 2.1 Ho, Pak Tung, \"A first eigenvalue estimate for embedded hypersurfaces\". Differential Geom. Appl. 26 (2008), no. 3, 273-276.) does not look right. Therefore, the author has decided to withdraw the paper",
  "categories": [
    "math.DG"
  ],
  "abstract": "The main point of this paper is that, under suitable conditions on the mean curvature and the Ricci curvature of the ambient space, we can extend Choi-Schoen's Compactness Theorem to compact embedded minimal surfaces to simple immersed compact H-surfaces in a Riemannian manifold with positive Ricci curvature (the mean curvature small depending on the Ricci curvature). Also, we prove that the space of convex embedded (fixed) constant mean curvature hypersurfaces in a simply connected 1/4-pinched manifold is compact.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-08-29T15:06:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10",
      "53C21",
      "47H11"
    ],
    "keywords": [
      "constant mean curvature surfaces",
      "compact riemannian manifolds",
      "ricci curvature",
      "constant mean curvature hypersurfaces",
      "extend choi-schoens compactness theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.3150E"
    }
  }
}