Quasiconformal Extensions of Harmonic Univalent Mappings of the Unit Disk
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866911130251689984 |
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| author | Ma, Xiu-Shuang |
| author_facet | Ma, Xiu-Shuang |
| contents | This note examines sufficient conditions for the quasiconformal extendibility of harmonic mappings defined in the unit disk. It is demonstrated that a harmonic strongly starlike mapping admits a quasiconformal extension to the entire plane, and an explicit formulation of its extension function is provided. Additionally, the quasiconformal extendibility of harmonic mappings defined in the exterior of the unit disk is explored. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_10022 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Quasiconformal Extensions of Harmonic Univalent Mappings of the Unit Disk Ma, Xiu-Shuang Complex Variables Primary 30C55, Secondary 30C62, 31A05 This note examines sufficient conditions for the quasiconformal extendibility of harmonic mappings defined in the unit disk. It is demonstrated that a harmonic strongly starlike mapping admits a quasiconformal extension to the entire plane, and an explicit formulation of its extension function is provided. Additionally, the quasiconformal extendibility of harmonic mappings defined in the exterior of the unit disk is explored. |
| title | Quasiconformal Extensions of Harmonic Univalent Mappings of the Unit Disk |
| topic | Complex Variables Primary 30C55, Secondary 30C62, 31A05 |
| url | https://arxiv.org/abs/2108.10022 |