{
  "id": "1802.03521",
  "version": "v1",
  "published": "2018-02-10T05:17:53.000Z",
  "updated": "2018-02-10T05:17:53.000Z",
  "title": "Self-similar solutions of curvature flows in warped products",
  "authors": [
    "Shanze Gao",
    "Hui Ma"
  ],
  "comment": "19 pages",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this paper we study self-similar solutions in warped products satisfying $F-\\mathcal{F}=\\bar{g}(\\lambda(r)\\partial_{r},\\nu)$, where $\\mathcal{F}$ is a nonnegative constant and $F$ is in a class of general curvature functions including powers of mean curvature and Gauss curvature. We show that slices are the only closed strictly convex self-similar solutions in the hemisphere for such $F$. We also obtain a similar uniqueness result in hyperbolic space $\\mathbb{H}^{3}$ for Gauss curvature $F$ and $\\mathcal{F}\\geq 1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-10T05:17:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "53C40"
    ],
    "keywords": [
      "warped products",
      "curvature flows",
      "gauss curvature",
      "similar uniqueness result",
      "general curvature functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}