The p-Weil-Petersson Teichmueller space and the quasiconformal extension of curves
The p-Weil-Petersson Teichmueller space and the quasiconformal extension of curves
复制标题
p-Weil-Petersson Teichmueller 空间和曲线的拟共形扩展
DOI：
10.1007/s12220-022-00946-8
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Matsuzaki Katsuhiko
中科院分区：
文献类型：
--
作者：
Wei Huaying;Matsuzaki Katsuhiko
我们考虑平面上的p-Weil-Petersson曲线空间与实直线上的p-Besov空间之间的对应关系。我们证明了利用热核定义的Beurling-Ahlfors扩张的变体产生了p-Besov空间的区域上到p-可积Beltrami系数空间的全纯映射。特别地，这给出了从p-可积Beltrami系数空间到p-Weil-Petersson Teichmüler空间的Teichmüler投影的整体实解析截面。
We consider the correspondence between the space ofp-Weil–Petersson curveson the plane and thep-Besov space ofon the real line for. We prove that the variant of the Beurling–Ahlfors extension defined by using the heat kernel yields a holomorphic map foruon a domain of thep-Besov space to the space ofp-integrable Beltrami coefficients. This in particular gives a global real-analytic section for the Teichmüller projection from the space ofp-integrable Beltrami coefficients to thep-Weil–Petersson Teichmüller space.