论文标题
Weil-Petersson距离上的一个新的均匀下限
A new uniform lower bound on Weil-Petersson distance
论文作者
论文摘要
在本文中，我们研究了基于Weil-Petersson大地测量学的固定点的注射率半径。我们表明，基于固定点的注射率半径的平方根为$ 0.3884 $ -LIPSCHITZ在带有Weil-Petersson Metric的Teichmüller空间上。作为应用程序，我们谴责收缩函数的平方根在带有Weil-Petersson指标的Teichmüller空间上均匀地是Lipschitz，在那里可以选择Lipschitz常数为$ 0.5492 $。还将讨论用于大属的Riemann表面模量空间的渐近几何形状的应用。
In this paper we study the injectivity radius based at a fixed point along Weil-Petersson geodesics. We show that the square root of the injectivity radius based at a fixed point is $ 0.3884$-Lipschitz on Teichmüller space endowed with the Weil-Petersson metric. As an application we reprove that the square root of the systole function is uniformly Lipschitz on Teichmüller space endowed with the Weil-Petersson metric, where the Lipschitz constant can be chosen to be $0.5492$. Applications to asymptotic geometry of moduli space of Riemann surfaces for large genus will also be discussed.
