Bao-Hua Xie

activity

20222026

collaborators

6 papers

math.GT2026

Delambre--Gauss Formulas in Complex Hyperbolic Space

Jiming Ma, Baohua Xie

We establish a Delambre--Gauss matrix identity for oriented right-angled hexagons in the complex hyperbolic plane. The six complex length parameters of a hexagon determine two alte…

math.GT2026

Spherical CR uniformizations of a sequence of hyperbolic 3-manifolds

Jiming Ma, Baohua Xie

Let $s 782$ be the 2-cusped hyperbolic 3-manifold in the SnapPy census. Its spherical CR uniformization was established in \cite{JWX2023} using the Ford domain of the complex hyperb…

math.GT2024

Complex Hyperbolic Geometry of Chain Links

Jiming Ma, Baohua Xie, Mengmeng Xu

The complex hyperbolic triangle group $Γ = Δ_{4, \infty, \infty; \infty}$ acting on the complex hyperbolic plane $H_{C}^{2}$ is generated by complex reflections $I_{1}$ , $I_{2}$ …

math.GT2023

Figure-eight knot is always over there

Jiming Ma, Baohua Xie

It is well-known that complex hyperbolic triangle groups $Δ (3, 3, 4)$ generated by three complex reflections $I_{1}, I_{2}, I_{3}$ in $\mbox{PU(2,1)}$ has 1-dimensional moduli space. Deformi…

math.GT2023

The topology of the Eisenstein-Picard modular surface

Jiming Ma, Baohua Xie

The Eisenstein-Picard modular surface $M$ is the quotient space of the complex hyperbolic plane by the modular group $PU (2, 1; Z [ω])$ . We determine the global topology…

math.GT2022

Menger curve and Spherical CR uniformization of a closed hyperbolic 3-orbifold

Jiming Ma, Baohua Xie

Let $G_{6, 3} = ⟨ a_{0}, \dots, a_{5} ∣ a_{i}^{3} = i d, a_{i} a_{i + 1} = a_{i + 1} a_{i}, i \in Z /6 Z ⟩$ be a hyperbolic group with boundary the Menger curve. J. G…