| 渐近Teichmüller空间的不唯一性 |
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| 引用本文： | 黄志勇,周泽民. 渐近Teichmüller空间的不唯一性[J]. 数学学报, 2019, 62(5): 703-708 |
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| 作者姓名： | 黄志勇 周泽民 |
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| 作者单位： | 中国人民大学数学系 北京 100872 |
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| 基金项目： | 国家自然科学基金资助项目（11571362，11371045） |
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| 摘 要： | 设AT(△)是单位圆盘△上所有渐近Teichmüller等价类[[μ]]或[[f~μ]]构成的渐近Teichmüller空间.本文证明了对AT(△)内的任意渐近极值的f~μ,总存在一个[[f~μ]]内的渐近极值映射g~v,使边界伸缩商h~*(μ_(fog)~(-1)(g(z)))≠0.同时也获得了AT(△)在基点处的切空间上的类似结果.
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| 关 键 词： | Teichmüller空间 拟共形映射 极值映射 渐近Teichmüller空间 |
Nonuniqueness Properties on Asymptotic Teichmuller Space |
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| Zhi Yong HUANG,Ze Min ZHOU. Nonuniqueness Properties on Asymptotic Teichmuller Space[J]. Acta Mathematica Sinica, 2019, 62(5): 703-708 |
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| Authors: | Zhi Yong HUANG Ze Min ZHOU |
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| Affiliation: | Department of Mathematics, Renmin University of China, Beijing 100872, P. R. China |
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| Abstract: | Let AT (Δ) be the asymptotic Teichmüller space on the unit disk Δ, viewed as the space of all asymptotic Teichmüller equivalence classes[[μ]] or[[f μ]]. It is shown that, for each asymptotically extremal[[f μ]] in AT (Δ), there exists an asymptotically extremal gν in[[f μ]] such that the boundary dilatation h*(μf?g-1(g(z))) =0. A parallel result in the tangent space to AT (Δ) at the basepoint is also obtained. |
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| Keywords: | Teichmüller space quasiconformal mappings extremal quasiconformal mappings asymptotic Teichmüller space |
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