The Stable Neighborhood Theorem and Lengths of Closed Geodesics
The Stable Neighborhood Theorem and Lengths of Closed Geodesics
We derive a generalized collar lemma, called the stable neighborhood theorem, for nonsimple closed geodesics. As an application, we show that there is a lower bound for the length of a closed geodesic having crossing number $k$ on a hyperbolic surface. This lower bound only depends on $k$ and tends …