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Minimal length of two intersecting simple closed geodesics

Thomas Gauglhofer·Hugo Parlier
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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 $n\leq 3$.

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Thomas Gauglhofer, Hugo Parlier. 2006-08-14. Minimal length of two intersecting simple closed geodesics. https://arxiv.org/abs/math/0608049

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