2020/11/27 by Nick Bell, Bell, Nick
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2011.13969
openalex publication_date 2020/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 L6g-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.