Arcwise Connected Domains, Quasiconformal Mappings, and Quasidisks
We prove that a homeomorphism f:R2→R2 is a quasiconformal mapping if and only if f(D) is an arcwise connected domain for any arcwise connected domain D⊆R2, and D is a quasidisk if and only if both D and its exterior D*=R2∖D¯ are arcwise connected domains.
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/419850 |
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| _version_ | 1832549532570746880 |
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| author | Yu-Ming Chu |
| author_facet | Yu-Ming Chu |
| author_sort | Yu-Ming Chu |
| collection | DOAJ |
| description | We prove that a homeomorphism f:R2→R2 is a quasiconformal mapping if and only if f(D) is an arcwise connected domain for any arcwise connected domain D⊆R2, and D is a quasidisk if and only if both D and its exterior D*=R2∖D¯ are arcwise connected domains. |
| format | Article |
| id | doaj-art-a25a4fc6a8c74a1aa2ccd37a90e18a74 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a25a4fc6a8c74a1aa2ccd37a90e18a742025-02-03T06:11:03ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/419850419850Arcwise Connected Domains, Quasiconformal Mappings, and QuasidisksYu-Ming Chu0School of Mathematics and Computation Sciences, Hunan City University, Yiyang 413000, ChinaWe prove that a homeomorphism f:R2→R2 is a quasiconformal mapping if and only if f(D) is an arcwise connected domain for any arcwise connected domain D⊆R2, and D is a quasidisk if and only if both D and its exterior D*=R2∖D¯ are arcwise connected domains.http://dx.doi.org/10.1155/2014/419850 |
| spellingShingle | Yu-Ming Chu Arcwise Connected Domains, Quasiconformal Mappings, and Quasidisks Abstract and Applied Analysis |
| title | Arcwise Connected Domains, Quasiconformal Mappings, and Quasidisks |
| title_full | Arcwise Connected Domains, Quasiconformal Mappings, and Quasidisks |
| title_fullStr | Arcwise Connected Domains, Quasiconformal Mappings, and Quasidisks |
| title_full_unstemmed | Arcwise Connected Domains, Quasiconformal Mappings, and Quasidisks |
| title_short | Arcwise Connected Domains, Quasiconformal Mappings, and Quasidisks |
| title_sort | arcwise connected domains quasiconformal mappings and quasidisks |
| url | http://dx.doi.org/10.1155/2014/419850 |
| work_keys_str_mv | AT yumingchu arcwiseconnecteddomainsquasiconformalmappingsandquasidisks |