Author

X. Han

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Preprint Aug 2026

Growth of Simple Closed Geodesics in Finite-Volume Hyperbolic Manifolds

Let $M$ be a finite-volume hyperbolic $d$-manifold with $d\ge3$. We prove that the number of primitive nonsimple closed geodesics has exponential growth rate strictly smaller than $d-1$. Consequently, asymptotically almost every primitive closed geodesic in $M$ is simple. In contrast, we show that on an arithmetic hype...

X. Han, Bo-Han Yang · 0 citations