Bers同时单值化与庞加莱和乐簇的交

A 1-parameter family of spherical CR uniformizations of the figure eight knot complement

We describe a simple fundamental domain for the holonomy group of the boundary unipotent spherical CR uniformization of the figure eight knot complement, and deduce that small deformations of that holonomy group (such that the boundary holonomy remains parabolic) also give a uniformization of the figure eight knot complement. Finally, we construct an explicit 1-parameter family of deformations of the boundary unipotent holonomy group such that the boundary holonomy is twist-parabolic. For small values of the twist of these parabolic elements, this produces a 1-parameter family of pairwise non-…

Projective structures with degenerate holonomy and the Bers density conjecture

We prove the Bers' density conjecture for singly degenerate Kleinian surfaces groups without parabolics.

On spherical CR uniformization of 3-manifolds

We consider the discrete representations of 3-manifold groups into $PU(2,1)$ that appear in the Falbel-Koseleff-Rouillier census, such that the peripheral subgroups have cyclic unipotent holonomy. We show that two of these representations have conjugate images, even though they represent different 3-manifold groups. This illustrates the fact that a discrete representation $π_1(M)\rightarrow PU(2,1)$ with cyclic unipotent boundary holonomy is not in general the holonomy of a spherical CR uniformization of $M$.

同时均匀化与代数对应

Simultaneous Uniformization and Algebraic Correspondences

本文将Bers同时均匀化定理推广到代数对应框架，构造了同时均匀化一对非拓扑同胚的零亏格轨道形的代数对应，并给出穿孔球面Teichmüller空间的复解析实现。

复仿射球面与 SL(3,C) 的 Bers 定理

Complex affine spheres and a Bers theorem for SL(3,C)

本文利用复仿射球面、bi-Higgs 丛及复椭圆 PDE，构造 Hitchin 表示对上的等变全纯映射，将 Bers 同时单值化推广到 SL(3,C) 特征标簇。

Teichmüller 理论中的二次微分与复调和映射

Quadratic differentials in Teichmüller theory and complex harmonic maps

本文证明三个经典的 Teichmüller 空间映射均为同一局部双全纯映射的限制，并构造其右逆，同时发展复调和映射理论，获得 Deligne-Hitchin 模空间中扭线的几何解释。