论文标题
简单的长度光谱作为双曲线表面的模量和长度身份的刚性
Simple length spectra as moduli for hyperbolic surfaces and rigidity of length identities
论文作者
论文摘要
在本文中，我们重新访问了双曲线表面上简单的封闭曲线所享有的经典长度身份。我们陈述并证明了此类身份在Teichmüller空间上的刚性。由于这种刚度，某些简单的封闭曲线的集合最小的相交的曲线以其长度在通用双曲线表面上表征。 作为一个应用程序，我们在可拓扑定向的表面$ s $的Teichmüller空间中构建了微薄的$ v $，可能是无限类型的。然后，$ v $ $ s $上的（nielsen-convex）双曲线结构的等轴测类别的特征是其未标记的简单长度光谱。即，我们表明简单的长度光谱可以用作通用双曲线表面的模量。在紧凑型表面的情况下，通过Wolpert获得了使用长度光谱的类似结果。
In this article, we revisit classical length identities enjoyed by simple closed curves on hyperbolic surfaces. We state and prove the rigidity of such identities over Teichmüller spaces. Due to this rigidity, certain collections of simple closed curves which minimally intersect are characterized on generic hyperbolic surfaces by their lengths. As an application, we construct a meagre set $V$ in the Teichmüller space of a topological orientable surface $S$, possibly of infinite type. Then the isometry class of a (Nielsen-convex) hyperbolic structure on $S$ outside $V$ is characterized by its unmarked simple length spectrum. Namely, we show that the simple length spectra can be used as moduli for generic hyperbolic surfaces. In the case of compact surfaces, an analogous result using length spectra was obtained by Wolpert.
