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 language | English |
|---|---|
| Pages (from-to) | 391-402 |
| Number of pages | 12 |
| Journal | Filomat |
| Volume | 27 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2013 |
| Externally published | Yes |
Keywords
- Closed quasiregular mapping
- Conformal modulus
- Maximal (minimal) multiplicity
- Property P
- Property P
- Quasiball
- Quasiconformal mapping
- Quasiregular mapping