Qiliang Luo

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math.GT2026

Simple geodesics in closed hyperbolic manifolds

Qiliang Luo, Vladimir Marković

Given any closed hyperbolic n-manifold M ( $n \geq 3$ ), 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…

math.GT2026

On the minimal diameter of finite covers

Yifei Cai, Qiliang Luo

We prove that every closed hyperbolic surface admits a sequence of finite covers with asymptotically optimal diameters.

math.GT2026

The Effective Ehrenpreis Conjecture

Qiliang Luo

Let $M$ and $N$ be two closed hyperbolic Riemann surfaces. The Ehrenpreis Conjecture (proved by Kahn-Markovic) asserts that for any $ε > 0$ there are finite covers $M_{ε} \to M$ , and $N…