{
  "id": "1512.02732",
  "version": "v1",
  "published": "2015-12-09T02:55:29.000Z",
  "updated": "2015-12-09T02:55:29.000Z",
  "title": "Exhaustion of isoperimetric regions in asymptotically hyperbolic manifolds with scalar curvature $R\\geq -6$",
  "authors": [
    "Dandan Ji",
    "Yuguang Shi",
    "Bo Zhu"
  ],
  "comment": "25pages, no figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, aimed at exploring the fundamental properties of isoperimetric region in $3$-manifold $(M^3,g)$ which is asymptotic to Anti-de Sitter-Schwarzschild manifold with scalar curvature $R\\geq -6$, we prove that connected isoperimetric region $\\{D_i\\}$ with $\\mathcal{L}_g ^3(D_i)\\geq \\delta_0>0$ cannot slide off to infinity provided $(M^3,g)$ is not isometric to the hyperbolic space. Furthermore, we prove that isoperimetric region $\\{D_i\\}$ with topological sphere $\\{\\partial D_i\\}$ is exhausting regions of $M$ if Hawking mass $m_H(\\partial D_i)$ has uniform bound. Under the case of exhausting isoperimetric region , we obtain a formula on expansion of isoperimetric profile in terms of renormalized volume.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-09T02:55:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "83C57",
      "53C44"
    ],
    "keywords": [
      "asymptotically hyperbolic manifolds",
      "scalar curvature",
      "exhaustion",
      "anti-de sitter-schwarzschild manifold",
      "fundamental properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}