{
  "id": "2304.01769",
  "version": "v1",
  "published": "2023-04-04T12:59:27.000Z",
  "updated": "2023-04-04T12:59:27.000Z",
  "title": "Riemannian Penrose inequality without horizon in dimension three",
  "authors": [
    "Jintian Zhu"
  ],
  "comment": "16 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "Based on the $\\mu$-bubble method we are able to prove the following version of Riemannian Penrose inequality without horizon: if $g$ is a complete metric on $\\mathbb R^3\\setminus\\{O\\}$ with nonnegative scalar curvature, which is asymptotically flat around the infinity of $\\mathbb R^3$, then the ADM mass $m$ at the infinity of $\\mathbb R^3$ satisfies $m\\geq \\sqrt{\\frac{A_g}{16\\pi}}$, where $A_g$ is denoted to be the area infimum of embedded closed surfaces homologous to $\\mathbb S^2(1)$ in $\\mathbb R^3\\setminus\\{O\\}$. Moreover, the equality holds if and only if there is a strictly outer-minimizing minimal $2$-sphere such that the region outside is isometric to the half Schwarzschild manifold with mass $\\sqrt{\\frac{A_g}{16\\pi}}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-04T12:59:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "53C24"
    ],
    "keywords": [
      "riemannian penrose inequality",
      "half schwarzschild manifold",
      "region outside",
      "complete metric",
      "equality holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}