On Koebe-type functions for harmonic quasiconformal mappings
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914229059059712 |
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| author | Wang, Zhi-Gang Qiu, Jia-Le Rasila, Antti |
| author_facet | Wang, Zhi-Gang Qiu, Jia-Le Rasila, Antti |
| contents | This paper studies a class of Koebe-type harmonic quasiconformal functions. It is motivated by the shear construction of Clunie and Sheil-Small [Ann. Acad. Sci. Fenn. Ser. A I Math. 9: 3--25, 1984] and the harmonic quasiconformal Koebe function. Equivalent univalence conditions, pre-Schwarzian and Schwarzian norms, coefficient inequalities, as well as growth and area theorems for this family of functions are established. These findings improve several previously known results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12562 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Koebe-type functions for harmonic quasiconformal mappings Wang, Zhi-Gang Qiu, Jia-Le Rasila, Antti Complex Variables 31A05, 30C55, 30C62 This paper studies a class of Koebe-type harmonic quasiconformal functions. It is motivated by the shear construction of Clunie and Sheil-Small [Ann. Acad. Sci. Fenn. Ser. A I Math. 9: 3--25, 1984] and the harmonic quasiconformal Koebe function. Equivalent univalence conditions, pre-Schwarzian and Schwarzian norms, coefficient inequalities, as well as growth and area theorems for this family of functions are established. These findings improve several previously known results. |
| title | On Koebe-type functions for harmonic quasiconformal mappings |
| topic | Complex Variables 31A05, 30C55, 30C62 |
| url | https://arxiv.org/abs/2505.12562 |