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On a Theorem of Schwarz Type for Quasiconformal Mappings in Space
| Content Provider | Scilit |
|---|---|
| Author | Ikoma, Kazuo |
| Copyright Year | 1967 |
| Description | A space ring R is defined as a domain whose complement in the Moebius space consists of two components. The modulus of R can be defined in variously different but essentially equivalent ways (see e.g. Gehring [3] and Krivov [5]), which is denoted by mod R. Following Gehring [2], we refer to a homeomorphism y(x) of a space domain D as a k-quasiconformal mapping, if the modulus conditionis satisfied for all bounded rings R with their closure , where y(R) denotes the image of R by y = y(x). Then, it is evident that the inverse of a k-quasi-conformal mapping is itself k-quasiconformal and that a $k_{1}$-quasiconformal mapping followed by a $k_{2}$-quasiconformal one is $k_{1}k_{2}$-quasiconformal. It is also well known that the restriction of a Moebius transformation to a space domain is equivalent to a 1-quasiconformal mapping of its domain. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/7EB90FF21CA966770D142E8F9F04FC2E/S0027763000024107a.pdf/div-class-title-on-a-theorem-of-schwarz-type-for-quasiconformal-mappings-in-space-div.pdf |
| Ending Page | 30 |
| Page Count | 12 |
| Starting Page | 19 |
| ISSN | 00277630 |
| e-ISSN | 21526842 |
| DOI | 10.1017/s0027763000024107 |
| Journal | Nagoya Mathematical Journal |
| Volume Number | 29 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1967-03-01 |
| Access Restriction | Open |
| Subject Keyword | Nagoya Mathematical Journal Quasiconformal Mapping |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
