On the elliptic harmonic mappings and sense-preserving harmonic mappings
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914749178970112 |
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| author | Liu, Ming-Sheng XU, Hao |
| author_facet | Liu, Ming-Sheng XU, Hao |
| contents | In this paper, we first establish two versions of Landau-Bloch type theorem for $(K,K')$-elliptic harmonic mappings with a bounded minimum distortion. Next, we provide several coefficient estimates and a conjecture for $(K,K')$-elliptic harmonic mappings. Then, we establish three new versions of Landau-Bloch type theorem for sense-preserving harmonic mappings. Finally, we establish two sharp versions of Landau-Bloch type theorem for certain harmonic mappings. These results are sharp in some given cases and improve the related results of different authors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07666 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the elliptic harmonic mappings and sense-preserving harmonic mappings Liu, Ming-Sheng XU, Hao Complex Variables Primary 30C50, 31A05, Secondary 32A18, 30C62, 33E05 In this paper, we first establish two versions of Landau-Bloch type theorem for $(K,K')$-elliptic harmonic mappings with a bounded minimum distortion. Next, we provide several coefficient estimates and a conjecture for $(K,K')$-elliptic harmonic mappings. Then, we establish three new versions of Landau-Bloch type theorem for sense-preserving harmonic mappings. Finally, we establish two sharp versions of Landau-Bloch type theorem for certain harmonic mappings. These results are sharp in some given cases and improve the related results of different authors. |
| title | On the elliptic harmonic mappings and sense-preserving harmonic mappings |
| topic | Complex Variables Primary 30C50, 31A05, Secondary 32A18, 30C62, 33E05 |
| url | https://arxiv.org/abs/2404.07666 |