| 王朝川,杨敏,冯小高.区域的Schwarz导数和对数导数单叶性内径[J].井冈山大学自然版,2024,45(5):1-8 |
| 区域的Schwarz导数和对数导数单叶性内径 |
| THE UNIVALENT INNER RADIUS OF THE SCHWARZ DERIVATIVE AND PRE-SCHWARZ DERIVATIVE OF THE DOMAIN |
| 投稿时间：2024-03-22 修订日期：2024-05-12 |
| DOI：10.3969/j.issn.1674-8085.2024.05.001 |
| 中文关键词: 单叶性内径 Schwarz导数 Pre-Schwarz导数 |
| 英文关键词: inner radius of univalence Schwarz derivative Pre-Schwarz derivative |
| 基金项目:国家自然科学基金项目(11701459，12271218) |
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| 摘要点击次数: 645 |
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| 中文摘要: |
| 利用Ahlfors所得关于解析函数单叶性与拟共形延拓的一般性公式，研究了单叶性内径问题。在角域和一般拟圆上得到Schwarz导数单叶性内径的几个下界估计公式。同时，在单位圆、上半平面、角域以及拟圆上，推广了对数导数单叶性内径的下界公式。 |
| 英文摘要: |
| The inner radius problem of univalence is studied by using the general formula of univalence and quasiconformal extension of analytic functions obtained by Ahlfors. We obtain several lower bounds for the inner radius of Schwarz derivative univalence on angular domain and general quasicircle. At the same time, on the unit circle, the upper half plane, the angular domain and the quasi-circle, the lower bound formula of the inner radius of the Pre-Schwarz derivative univalence is generalized. |
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