Quasiconformal Extensions and Inner Radius of Univalence by pre-Schwarzian Derivatives of Analytic and Harmonic Mappings
In this paper, we study the criterion for univalence, quasiconformal extensions and inner radius of univalence for locally univalent analytic and harmonic mappings in the complex plane. For locally univalent analytic functions in the unit disk, we give a sufficient condition for univalence and quasi...
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| Datum: | 2023 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2023
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| Online Zugang: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1040 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Zusammenfassung: | In this paper, we study the criterion for univalence, quasiconformal extensions and inner radius of univalence for locally univalent analytic and harmonic mappings in the complex plane. For locally univalent analytic functions in the unit disk, we give a sufficient condition for univalence and quasiconformal extensions by pre-Schwarzian derivatives, which generalizes Becker's result. For strongly spirallike domains, we consider the quasiconformal extension and obtain the lower bounds of the inner radius of univalence by pre-Schwarzian derivatives and Schwarzian derivatives. Furthermore, for harmonic mappings in a simply connected domain $\Omega$, we prove that $\Omega$ is a quasidisk if and only if the inner radius of univalence of the domain $\Omega$ by pre-Schwarzian derivatives of harmonic mappings is positive, and we obtain a general sufficient condition for univalence and quasiconformal extensions.
Mathematical Subject Classification 2020: 30C62, 30C45, 30C55, 31A05 |
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