Year: 2026
Type: preprint
Abstract: Given any closed hyperbolic n-manifold M ($n\ge 3$), we show that for a fixed $κ>\frac{3}{n-2}$, a random closed geodesic of length close to r has the collar of width $r^{-κ}$ when r is large enough. In particular, most closed geodesics of length close to r are simple. This theorem positively answers Problem 3.16 from Kirby's list which asks whether every closed hyperbolic 3-manifold contains infinitely many simple closed geodesics.
Source: arXiv (Cornell University)
Authors: Luo, Qiliang, Marković, Vladimir
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204918634