Minimal length of two intersecting simple closed geodesics

2006/08/02 by Thomas Gauglhofer, Gauglhofer, Thomas, Hugo Parlier +1
Computer Science · Engineering · Mathematics · #30F20 #30F45 #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematics and Applications #math.DG #math.GT #msc:30F20 #msc:30F45

paper · pdf · doi:10.48550/arxiv.math/0608049

Typos corrected

openalex publication_date 2006/08/02 · arxiv created 2006/08/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

On a hyperbolic Riemann surface, given two simple closed geodesics that intersect n times, we address the question of a sharp lower bound L_n on the length attained by the longest of the two geodesics. We show the existence of a surface S_n on which there exists two simple closed geodesics of length L_n intersecting n times and explicitly find L_n for n≤ 3.

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