39 citations · 66 across the 23 of their papers we have counts for
24 papers
Spherical harmonics with maximal Lp norm growth
Xiaolong Han
In this paper, we show that for every p>2, there is an orthonormal basis of spherical harmonics on Sn with n>=2 which achieves the maximal Lp norm growth. More precisely, one basis…
Growth of Simple Closed Geodesics in Finite-Volume Hyperbolic Manifolds
Xiaolong Hans Han, Bohan Yang
Let be a finite-volume hyperbolic -manifold with . We prove that the number of primitive nonsimple closed geodesics has exponential growth rate strictly smaller than…
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…
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 commensurabili…
Large Steklov eigenvalues on hyperbolic surfaces
Xiaolong Hans Han, Yuxin He, Han Hong
In this paper, we first construct a sequence of hyperbolic surfaces with connected geodesic boundary such that the first normalized Steklov eigenvalue tends to infinity…
Spherical harmonics and point configurations on the sphere
Xiaolong Han
We construct spherical harmonics on the two-dimensional unit sphere as superpositions of Gaussian beams whose poles form well-separated point configurations. The distributional and…