闭双曲流形中的简单测地线

中文摘要 AI 辅助

给定任意闭双曲n-流形M（n≥3），我们证明，对于固定的κ>3/(n-2)，当r足够大时，长度接近r的随机闭测地线具有宽度为r^(-κ)的领圈。特别地，大部分长度接近r的闭测地线是简单的。该定理正面回答了Kirby列表中的问题3.16，该问题询问每个闭双曲3-流形是否包含无穷多简单闭测地线。

英文摘要

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.

发表机构

• YMSC Tsinghua University（清华大学高等研究院）

机构由 AI 辅助整理，请以论文原文为准。