{
  "id": "2107.01756",
  "version": "v1",
  "published": "2021-07-05T01:49:27.000Z",
  "updated": "2021-07-05T01:49:27.000Z",
  "title": "Lower and upper order of harmonic mappings",
  "authors": [
    "Arbeláez",
    "H.",
    "Hernández",
    "R.",
    "Sierra W"
  ],
  "categories": [
    "math.CV"
  ],
  "abstract": "In this paper, we define both the upper and lower order of a sense-preserving harmonic mapping in $\\mathbb{D}$. We generalize to the harmonic case some known results about holomorphic functions with positive lower order and we show some consequences of a function having finite upper order. In addition, we improve a related result in the case when there is equality in a known distortion theorem for harmonic mappings with finite upper order. Some examples are provided to illustrate the developed theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-05T01:49:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30C45",
      "30A10",
      "30C62"
    ],
    "keywords": [
      "harmonic mapping",
      "finite upper order",
      "positive lower order",
      "harmonic case",
      "distortion theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}