Closed geodesics on hyperbolic surfaces with few intersections

Abstract

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

12 pages, 4 figures