On Douady–Earle extension and the contractibility of the VMO-Teichmüller space☆
On Douady–Earle extension and the contractibility of the VMO-Teichmüller space☆
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DOI：
10.1016/j.jmaa.2016.04.073
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发表时间：
2016-10
影响因子：
1.3
通讯作者：
Shuan Tang;Huaying Wei;Yu-liang Shen
中科院分区：
文献类型：
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作者：
Shuan Tang;Huaying Wei;Yu-liang Shen
Douady-Earle扩张提供了拟对称同胚到单位圆盘的拟共形扩张，并导出了Beltrami系数的连续自映射σ.本文证明了σ在Beltrami系数上也是连续的（在更强的拓扑下），这些Beltrami系数导致Carleson测度为零，从而投射到VMO-Teichmüller空间.一个直接的结果是VMO-Teichmüller空间是可收缩的。
Douady–Earle extension provides a quasiconformal extension of a quasisymmetric homeomorphism to the unit disk and induces a continuous self-mapσof Beltrami coefficients. In this note, we show thatσis also continuous (under a stronger topology) on those Beltrami coefficients which induce vanishing Carleson measures and thus project to the VMO-Teichmüller space. An immediate consequence is that the VMO-Teichmüller space is contractible.