On Length Sets of Subarithmetic Hyperbolic Manifolds

Absolute profinite rigidity of some closed fibered hyperbolic 3-manifolds

We give the first examples of closed fibered hyperbolic 3-manifolds whose fundamental groups are distinguished from every other finitely generated, residually finite group by their finite quotients. One of the examples is also the first example of a non-orientable profinitely rigid hyperbolic 3-manifold.

紧双曲流形上测地周期的非零性

Nonvanishing of geodesic periods over compact hyperbolic manifolds

设$X$是一个维数为$d\geqslant3$的紧致双曲流形.本文证明了在$X$的任何紧$n$维（$n\geqslant2$）测地圈上定义有无穷多个非零测地周期.

Upper bounds for geodesic periods over hyperbolic manifolds

We prove an upper bound for geodesic periods of Maass forms over hyperbolic manifolds. By definition, such periods are integrals of Maass forms restricted to a special geodesic cycle of the ambient manifold, against a Maass form on the cycle. Under certain restrictions, the bound will be uniform.

Systoles of Arithmetic Hyperbolic 2- and 3-Manifolds

In this paper we study the systoles of arithmetic hyperbolic 2- and 3-manifolds. Our first result is the construction of infinitely many arithmetic hyperbolic 2- and 3-manifolds which are pairwise noncommensurable, all have the same systole, and whose volumes are explicitly bounded. Our second result fixes a positive number x and gives an upper bound for the least volume of an arithmetic hyperbolic 2- or 3-manifold whose systole is greater than x. We conclude by determining, for certain small values of x, the least volume of a principal arithmetic hyperbolic 2-manifold over Q or 3-manifold ove…

具有有界体积和迹场度II的双曲三流形

Hyperbolic three manifolds of bounded volume and trace field degree II

本文证明了作者在[2]中提出的有界高度猜想。作为推论，得出了只有有限个体积和迹场度有界的双曲三流形。

双曲流形上最小1-型Laplacian eigenvalue的几何

Geometry of the smallest 1-form Laplacian eigenvalue on hyperbolic manifolds

我们与小1-形式拉普拉斯特征值的相对闭链复杂性封闭双曲流形：小特征值对应于闭测地线没有多个边界的表面小亏格。我们描述了这一等价原理在证明双曲3-流形Benjamini-Schramm收敛到$\mathbb{H}^3.$的最优挠同调增长中的潜在应用