3 papers
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 contains a sequenc…
math.GT2026
Counting surface subgroups in cusped hyperbolic 3-manifolds
Xiaolong Hans Han, Zhenghao Rao, Jia Wan
Let be a finite-volume, noncompact hyperbolic 3-manifold. We show that the number of quasi-Fuchsian surface subgroups of (up to conjugacy and commensurabi…
math.CA2025
Spherical harmonics and point configurations on the sphere
Xiaolong Han
We develop a systematic framework for constructing spherical harmonics on the two-dimensional unit sphere as superpositions of Gaussian beams whose poles form well-separated point…