Integrably asymptotic affine homeomorphisms of the circle and Teichmüller spaces
Integrably asymptotic affine homeomorphisms of the circle and Teichmüller spaces
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DOI：
10.1007/bf02897849
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发表时间：
2000-03
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影响因子：
--
通讯作者：
G. Cui
中科院分区：
文献类型：
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作者：
G. Cui
单位圆S1的拟对称同胚称为可积渐近仿射，如果它允许一个拟共形扩张进入单位圆盘，使得它的复伸缩在单位圆盘上的Poincaré度量下平方可积.设QS*(S1)是这类映射的空间。本文给出了QS*(S1)中映射的一些刻划和性质。我们还证明了QS*(S1)/Möb(S1)是Weil-Petersson度量中diff(S1)/Möb(S1)的完备化。
A quasisymmetric homeomorphism of the unit circle S1is called integrably asymptotic affine if it admits a quasiconformal extension into the unit disk so that its complex dilatation is square integrable in the Poincaré metric on the unit disk. Let QS*(s1) be the space of such maps. Here we give some characterizations and properties of maps in QS*(S1). We also show that QS*(S1)/Möb (S1) is the completion of Diff(S1)/Möb(S1) in the Weil-Petersson metric.