Vladimir Markovi'c

Simple geodesics in closed hyperbolic manifolds

Given any closed hyperbolic n-manifold M ($n\ge 3$), we show that for a fixed $\kappa>\frac{3}{n-2}$, a random closed geodesic of length close to r has the collar of width $r^{-\kappa}$ when r is large enough. In particular, most closed geodesics of length close to r are simple. This theorem positively answers Problem...