Closed geodesics on hyperbolic surfaces with few intersections

2024/03/01 by Wujie Shen, Shen, Wujie
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2403.00243

openalex publication_date 2024/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

We prove that, if a closed geodesic Γ on a complete finite type hyperbolic surface has at least 2 self-intersections, then the length of Γ has an lower bound 2log(5+2√6), and the lower bound is sharp, attained on a corkscrew geodesic on a thrice punctured sphere.

Related

• Nonsimple closed geodesics with given intersection number on hyperbolic surfaces
• Minimal length of nonsimple closed geodesics on hyperbolic surfaces
• Short closed geodesics with self-intersections
• Short closed geodesics on cusped hyperbolic surfaces
• A geometric property of closed geodesics on hyperbolic surfaces