{
  "id": "0909.0590",
  "version": "v2",
  "published": "2009-09-03T08:29:49.000Z",
  "updated": "2009-09-24T09:15:40.000Z",
  "title": "Small surfaces of Willmore type in Riemannian manifolds",
  "authors": [
    "T. Lamm",
    "J. Metzger"
  ],
  "comment": "25 pages. Minor corrections",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this paper we investigate the properties of small surfaces of Willmore type in Riemannian manifolds. By \\emph{small} surfaces we mean topological spheres contained in a geodesic ball of small enough radius. In particular, we show that if there exist such surfaces with positive mean curvature in the geodesic ball $B_r(p)$ for arbitrarily small radius $r$ around a point $p$ in the Riemannian manifold, then the scalar curvature must have a critical point at $p$. As a byproduct of our estimates we obtain a strengthened version of the non-existence result of Mondino \\cite{Mondino:2008} that implies the non-existence of certain critical points of the Willmore functional in regions where the scalar curvature is non-zero.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-09-24T09:15:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemannian manifold",
      "small surfaces",
      "willmore type",
      "geodesic ball",
      "scalar curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.0590L"
    }
  }
}