标题： 最短填充闭合多测地线的渐进行为 显示英文标题

标题： Asymptotics of shortest filling closed multi-geodesics

摘要： 在本文中，我们研究了闭双曲曲面上最短填充闭多测地线的渐进行为，当系统长度$\to 0$或当亏格$\to \infty$时。 We first show that for a closed hyperbolic surface $X_g$ of genus $g$, the length of a shortest filling closed multi-geodesic of $X_g$ is uniformly comparable to $$\left(g+\sum\limits_{\textit{closed geodesic }\gamma\subset X_g, \ \ell(\gamma)<1}\log \left(\frac{1}{\ell(\gamma)}\right)\right).$$ As an application, we show that as $g\to \infty$, a Weil-Petersson random hyperbolic surface has a shortest closed multi-geodesic of length uniformly comparable to $g$. We also show that this is true for a random hyperbolic surface in the Brooks-Makover model. 显示英文摘要

摘要： In this paper, we investigate the asymptotics of shortest filling closed multi-geodesics of closed hyperbolic surfaces as systole $\to 0$ or as genus $\to \infty$. We first show that for a closed hyperbolic surface $X_g$ of genus $g$, the length of a shortest filling closed multi-geodesic of $X_g$ is uniformly comparable to $$\left(g+\sum\limits_{\textit{closed geodesic }\gamma\subset X_g, \ \ell(\gamma)<1}\log \left(\frac{1}{\ell(\gamma)}\right)\right).$$ As an application, we show that as $g\to \infty$, a Weil-Petersson random hyperbolic surface has a shortest closed multi-geodesic of length uniformly comparable to $g$. We also show that this is true for a random hyperbolic surface in the Brooks-Makover model.