The VMO-Teichmueller space and the variant of Beurling-Ahlfors extension by heat kernel
The VMO-Teichmueller space and the variant of Beurling-Ahlfors extension by heat kernel
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VMO-Teichmueller 空间和热核的 Beurling-Ahlfors 扩展变体
DOI：
10.1007/s00209-022-03104-6
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发表时间：
2022
影响因子：
0.8
通讯作者：
Matsuzaki Katsuhiko
中科院分区：
文献类型：
--
作者：
Wei Huaying;Matsuzaki Katsuhiko
利用February man等人（Ann Math 134：65 - 124，1991）引入的Beurling-Ahlfors热核扩张的变形，给出了VMO-Teichmüller空间上Teichmüller投影的实解析截面.在此基础上，我们证明了VMO-Teichmüller空间可以被赋予一个实解析等价于其复Banach流形结构的真实的Banach流形结构.我们还得到VMO-Teichmüller空间允许实解析压缩映射。
We give a real-analytic section for the Teichmüller projection onto the VMO-Teichmüller space by using the variant of Beurling–Ahlfors extension by heat kernel introduced by Fefferman et al. (Ann Math 134:65–124, 1991). Based on this result, we prove that the VMO-Teichmüller space can be endowed with a real Banach manifold structure that is real-analytically equivalent to its complex Banach manifold structure. We also obtain that the VMO-Teichmüller space admits a real-analytic contraction mapping.