{
  "id": "1905.03191",
  "version": "v1",
  "published": "2019-05-08T16:20:20.000Z",
  "updated": "2019-05-08T16:20:20.000Z",
  "title": "On the asymptotic Plateau problem for area minimizing surfaces in $\\mathbb{E}(-1,τ)$",
  "authors": [
    "Patrícia Klaser",
    "Ana Menezes",
    "Álvaro Ramos"
  ],
  "comment": "19 pages, 6 figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "We prove some existence and non-existence results for complete area minimizing surfaces in the homogeneous space $\\mathbb{E}(-1,\\tau)$. As one of our main results, we present sufficient conditions for a curve $\\Gamma$ in $\\partial_{\\infty} \\mathbb{E}(-1,\\tau)$ to admit a solution to the asymptotic Plateau problem, in the sense that there exists a complete area minimizing surface in $\\mathbb{E}(-1,\\tau)$ having $\\Gamma$ as its asymptotic boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-08T16:20:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10",
      "53C42"
    ],
    "keywords": [
      "asymptotic plateau problem",
      "complete area minimizing surface",
      "sufficient conditions",
      "non-existence results",
      "asymptotic boundary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}