Mapping problems for quasiregular mappings

Manzi Huang, Antti Rasila*, Xiantao Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We study images of the unit ball under certain special classes of quasiregular mappings. For homeomorphic, i.e., quasiconformal mappings problems of this type have been studied extensively in the literature. In this paper we also consider non-homeomorphic quasiregular mappings. In particular, we study (topologically) closed quasiregular mappings originating from the work of J. V̈ais̈al̈a and M. Vuorinen in 1970's. Such mappings need not be one-to-one but they still share many properties of quasiconformal mappings. The global behavior of closed quasiregular mappings is similar to the local behavior of quasiregular mappings restricted to a so-called normal domain.

Original languageEnglish
Pages (from-to)391-402
Number of pages12
JournalFilomat
Volume27
Issue number2
DOIs
StatePublished - 2013

Keywords

  • Closed quasiregular mapping
  • Conformal modulus
  • Maximal (minimal) multiplicity
  • Property P
  • Property P
  • Quasiball
  • Quasiconformal mapping
  • Quasiregular mapping

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