{
  "id": "0909.2042",
  "version": "v1",
  "published": "2009-09-10T20:08:09.000Z",
  "updated": "2009-09-10T20:08:09.000Z",
  "title": "Stable hypersurfaces with constant scalar curvature in Euclidean spaces",
  "authors": [
    "Hilário Alencar",
    "Walcy Santos",
    "Detang Zhou"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We obtain some nonexistence results for complete noncompact stable hyppersurfaces with nonnegative constant scalar curvature in Euclidean spaces. As a special case we prove that there is no complete noncompact strongly stable hypersurface $M$ in $\\mathbb{R}^{4}$ with zero scalar curvature $S_2$, nonzero Gauss-Kronecker curvature and finite total curvature (i.e. $\\int_M|A|^3<+\\infty$).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-10T20:08:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C42"
    ],
    "keywords": [
      "euclidean spaces",
      "nonzero gauss-kronecker curvature",
      "zero scalar curvature",
      "nonnegative constant scalar curvature",
      "finite total curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.2042A"
    }
  }
}