论文标题
带正方形的圆形同构圆形钻石剪切
Circle homeomorphisms with square summable diamond shears
论文作者
论文摘要
我们介绍并研究了圆圈同构（直至莫比乌斯变换）的同态形态的空间，这些空间在$ \ ell^2 $的情况下，相对于沿Farey Tessellation的边缘的模块化坐标。钻石剪切物与剪切坐标相关，也与Penner引入的装饰的Teichmüller空间的$ \logλ$长度密切相关。我们获得了将这个新类与圆形同质形态的Weil-Petersson类和Hölder类别进行比较的结果。我们还以无限的剪切和钻石剪切方式表达了Weil-Petersson度量张量和符号形式。
We introduce and the study the space of homeomorphisms of the circle (up to Möbius transformations) which are in $\ell^2$ with respect to modular coordinates called diamond shears along the edges of the Farey tessellation. Diamond shears are related combinatorially to shear coordinates, and are also closely related to the $\log Λ$-lengths of decorated Teichmüller space introduced by Penner. We obtain sharp results comparing this new class to the Weil-Petersson class and Hölder classes of circle homeomorphisms. We also express the Weil-Petersson metric tensor and symplectic form in terms of infinitesimal shears and diamond shears.
