{
  "id": "2101.06063",
  "version": "v1",
  "published": "2021-01-15T11:21:51.000Z",
  "updated": "2021-01-15T11:21:51.000Z",
  "title": "Minkowski Inequality on Asymptotically Conical manifolds",
  "authors": [
    "Luca Benatti",
    "Mattia Fogagnolo",
    "Lorenzo Mazzieri"
  ],
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this paper we consider Asymptotically Conical Riemannian manifolds $(M,g)$ of dimension $n\\geq 3$ with nonnegative Ricci curvature. For every open bounded subset $\\Omega\\subseteq M$ with smooth boundary we prove that \\begin{equation} \\left(\\frac{\\vert{\\partial \\Omega^*}\\vert}{\\vert{\\mathbb{S}^{n-1}}\\vert}\\right)^{\\!\\frac{n-2}{n-1}}\\mathrm{AVR}(g)^{\\frac{1}{n-1}}\\leq \\frac{1}{\\vert{\\mathbb{S}^{n-1}}\\vert}\\int\\limits_{\\partial \\Omega} \\left\\vert{ \\frac{\\mathrm{H}}{n-1}} \\right\\vert\\,\\mathrm{d} \\sigma , \\end{equation} where $\\mathrm{H}$ is the mean curvature of $\\partial \\Omega$, $\\mathrm{AVR}(g)$ is the asymptotic volume ratio of $(M,g)$ and $\\Omega^*$ is the strictly outward minimising hull of $\\Omega$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-15T11:21:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q10",
      "35A16",
      "53C21",
      "35B06",
      "53E10",
      "39B62",
      "31C15",
      "35B40"
    ],
    "keywords": [
      "asymptotically conical manifolds",
      "minkowski inequality",
      "asymptotic volume ratio",
      "asymptotically conical riemannian manifolds",
      "mean curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}