X. Han

activity

20132026

most citedSmall scale quantum ergodicity in negatively curved manifolds

39 citations · 66 across the 23 of their papers we have counts for

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4 papers · 1 filter

math.GT2026

Growth of Simple Closed Geodesics in Finite-Volume Hyperbolic Manifolds

Xiaolong Hans Han, Bohan Yang

Let $M$ be a finite-volume hyperbolic $d$ -manifold with $d \geq 3$ . We prove that the number of primitive nonsimple closed geodesics has exponential growth rate strictly smaller than…

math.GT2026

Asymptotically geodesic hypersurfaces and the fundamental groups of hyperbolic manifolds

Xiaolong Hans Han, Ruojing Jiang

We consider closed hypersurfaces smoothly immersed in hyperbolic manifolds up to homotopy and commensurability. We prove that if a closed hyperbolic manifold $M$ contains a sequenc…

math.GT2026

Counting surface subgroups in cusped hyperbolic 3-manifolds

Xiaolong Hans Han, Zhenghao Rao, Jia Wan

Let $M = H^{3} /Γ$ be a finite-volume, noncompact hyperbolic 3-manifold. We show that the number of quasi-Fuchsian surface subgroups of $Γ$ (up to conjugacy and commensurabili…

math.GT2020

Harmonic Forms, Minimal Surfaces and Norms on Cohomology of Hyperbolic $3$ -Manifolds

Xiaolong Hans Han

We bound the $L^{2}$ -norm of an $L^{2}$ harmonic $1$ -form in an orientable cusped hyperbolic $3$ -manifold $M$ by its topological complexity, measured by the Thurston norm, up to a cons…

Growth of Simple Closed Geodesics in Finite-Volume Hyperbolic Manifolds

Asymptotically geodesic hypersurfaces and the fundamental groups of hyperbolic manifolds

Counting surface subgroups in cusped hyperbolic 3-manifolds

Harmonic Forms, Minimal Surfaces and Norms on Cohomology of Hyperbolic 3-Manifolds

Harmonic Forms, Minimal Surfaces and Norms on Cohomology of Hyperbolic $3$ -Manifolds