论文标题
在双曲线表面计数弧线
Counting arcs on hyperbolic surfaces
论文作者
论文摘要
我们给出了具有边界的完全有限面积的双曲线表面上边界组件之间有界长度的（多）弧的渐近生长。具体而言，如果$ s $具有$ g $，$ n $边界组件和$ p $刺穿，则最多最多$ l $的每个纯映射类轨道轨道中的正盖弧数是渐近的，均为$ l^{6g-6+2（n+p）} $ bimess n dimess n n of。我们证明了尖齿之间的弧的类似结果，在该弧之间，我们将这种弧的长度定义为通过从表面上去除某些cuspidal区域获得的亚弧的长度。
We give the asymptotic growth of the number of (multi-)arcs of bounded length between boundary components on complete finite-area hyperbolic surfaces with boundary. Specifically, if $S$ has genus $g$, $n$ boundary components and $p$ punctures, then the number of orthogeodesic arcs in each pure mapping class group orbit of length at most $L$ is asymptotic to $L^{6g-6+2(n+p)}$ times a constant. We prove an analogous result for arcs between cusps, where we define the length of such an arc to be the length of the sub-arc obtained by removing certain cuspidal regions from the surface.
