Minimal length of two intersecting simple closed geodesics

Details Minimal length of two intersecting simple closed geodesics Minimal length of two intersecting simple closed geodesics

2006-08-02

arxiv.org/abs/math/0608049v2

Mathematics

Differential Geometry

Typos corrected

Scientific paper

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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