On Koebe radius and coefficients estimate for univalent harmonic mappings
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908347875196928 |
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| author | Borovikov, Mikhail |
| author_facet | Borovikov, Mikhail |
| contents | The problem on estimate of the Koebe radius for univalent harmonic mappings of the unit disk $\mathbb D=\{z\in\mathbb C : |z|<1\}$ is considered. For a subclass of harmonic mappings with the standard normalization and a certain growth estimate for analytic dilatation, we provide new estimate for the Koebe radius. New estimate for Taylor coefficients of the holomorphic part of a function from the subclass under consideration is obtained as a corollary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05526 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Koebe radius and coefficients estimate for univalent harmonic mappings Borovikov, Mikhail Complex Variables The problem on estimate of the Koebe radius for univalent harmonic mappings of the unit disk $\mathbb D=\{z\in\mathbb C : |z|<1\}$ is considered. For a subclass of harmonic mappings with the standard normalization and a certain growth estimate for analytic dilatation, we provide new estimate for the Koebe radius. New estimate for Taylor coefficients of the holomorphic part of a function from the subclass under consideration is obtained as a corollary. |
| title | On Koebe radius and coefficients estimate for univalent harmonic mappings |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2403.05526 |