{
  "id": "1703.07087",
  "version": "v1",
  "published": "2017-03-21T08:07:35.000Z",
  "updated": "2017-03-21T08:07:35.000Z",
  "title": "Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature",
  "authors": [
    "Heiko Kröner",
    "Julian Scheuer"
  ],
  "comment": "15 pages. Comments are welcome",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form $F^{-p}$, where $p>1$ and $F$ is a positive, strictly monotone, homogeneous of degree $1$ and concave curvature function. In particular this class includes the mean curvature $F=H$. We prove that a certain initial pinching condition is preserved and the properly rescaled hypersurfaces converge smoothly to the unit sphere.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-21T08:07:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperbolic space",
      "high powers",
      "pinched hypersurfaces",
      "concave curvature function",
      "convergence results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}