{
  "id": "1412.4248",
  "version": "v1",
  "published": "2014-12-13T15:55:29.000Z",
  "updated": "2014-12-13T15:55:29.000Z",
  "title": "Estimates for the dilatation of $σ$-harmonic mappings",
  "authors": [
    "Giovanni Alessandrini",
    "Vincenzo Nesi"
  ],
  "comment": "8 pages, to appear on Rendiconti di Matematica e delle sue applicazioni",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider planar $\\sigma$-harmonic mappings, that is mappings $U$ whose components $u^1$ and $u^2$ solve a divergence structure elliptic equation ${\\rm div} (\\sigma \\nabla u^i)=0$, for $i=1,2$. We investigate whether a locally invertible $ \\sigma$-harmonic mapping $U$ is also quasiconformal. Under mild regularity assumptions, only involving $\\det \\sigma$ and the antisymmetric part of $\\sigma$, we prove quantitative bounds which imply quasiconformality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-13T15:55:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30C62",
      "35J55"
    ],
    "keywords": [
      "harmonic mapping",
      "dilatation",
      "divergence structure elliptic equation",
      "mild regularity assumptions",
      "antisymmetric part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.4248A"
    }
  }
}