论文标题
meromorthic $ l^2 $在平面表面上功能
Meromorphic $L^2$ functions on flat surfaces
论文作者
论文摘要
我们证明了TeichmüllerGeodesic流的非均匀双曲线的定量版本。也就是说，在任何TeichMüller流线的每个点，我们都以无限光谱间隙为沿流量线的无限光谱间隙，以易于估计的平面表面上的几何量沿流量线的变化，该差距大于或等于平坦的基质。作为应用，我们在测量的叶子的独特遗传性方面加强了Treviño和Smith的结果，并根据其轴的位置在二次差异的模量空间中估算了伪anosov同型同态的光谱间隙。
We prove a quantitative version of the non-uniform hyperbolicity of the Teichmüller geodesic flow. Namely, at each point of any Teichmüller flow line, we bound the infinitesimal spectral gap for variations of the Hodge norm along the flow line in terms of an easily estimated geometric quantity on the flat surface, which is greater than or equal to the flat systole. As applications, we strengthen results of Treviño and Smith regarding unique ergodicity of measured foliations, and give an estimate for the spectral gaps of pseudo-Anosov homeomorphisms based on the location of their axes in the moduli space of quadratic differentials.
