{
  "id": "math/0610313",
  "version": "v1",
  "published": "2006-10-10T07:57:15.000Z",
  "updated": "2006-10-10T07:57:15.000Z",
  "title": "Constant $k$-curvature hypersurfaces in Riemannian manifolds",
  "authors": [
    "Fethi Mahmoudi"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "Rugang Ye proved the existence of a family of constant mean curvature hypersurfaces in an $m+1$-dimensional Riemannian manifold $(M^{m+1},g)$, which concentrate at a point $p_0$ (which is required to be a nondegenerate critical point of the scalar curvature), moreover he proved that this family constitute a foliation of a neighborhood of $p_0$. In this paper we extend this result to the other curvatures (the $r$-th mean curvature for $1\\le r\\le m$).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-10T07:57:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10",
      "53C12",
      "35J20"
    ],
    "keywords": [
      "constant mean curvature hypersurfaces",
      "th mean curvature",
      "dimensional riemannian manifold",
      "rugang ye",
      "nondegenerate critical point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10313M"
    }
  }
}