Chang-Shou Lin

activity

20242026

collaborators

8 papers

math.AP2026

Geometric analysis on rhombus torus: Green function with two singularities

Zhijie Chen, Erjuan Fu, Chang-Shou Lin +1

Let $G (z)$ be the Green function on the flat torus $E_{τ} = C / (Z + Z τ)$ with the singularity at $0$ . Lin and Wang (Ann. Math. 2010) proved that $G (z)$ has at m…

math.AP2026

Classification of spherical metrics on tori with four singularities, I: half periods

Erjuan Fu, Chang-Shou Lin

Classifying the spherical metrics on a torus $E_{τ}$ with $4 π$ conic angle at each half period point\, $ω_{k} / 2, k = 0, 1, 2, 3$ \, is equivalent to classify solutions of the following c…

math.CA2026

On monodromy and spectral geometry of generalized Lamé equations with four singularities, I: half periods

Erjuan Fu, Chang-Shou Lin

We consider the unitary monodromy problem of the following generalized Lamé equations with apparent parameters \begin{equation*} y^{\prime\prime}(z)=\left(\frac{3}{4}\sum_{k=0}^3\w…

math.AP2025

Green functions, Hitchin's formula and curvature equations on tori II: Rectangular torus

Zhijie Chen, Erjuan Fu, Chang-Shou Lin

Let $G (z)$ be the Green function on the flat torus $E_{τ} = C / (Z + Z τ)$ with the singularity at $0$ . Lin and Wang (Ann. Math. 2010) proved that $G (z)$ has eith…

math.AP2025

Green functions, Hitchin's formula and curvature equations on tori

Zhijie Chen, Erjuan Fu, Chang-Shou Lin

Let $G (z) = G (z; τ)$ be the Green function on the flat torus $E_{τ} = C / (Z + Z τ)$ with the singularity at $0$ . Lin and Wang (Ann. Math. 2010) proved that $G (z)$ h…

math.AP2025

Sovability of curvature equations with multiple singular sources on torus via Painleve VI equations

Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin

We study the curvature equation with multiple singular sources on a torus \[Δu+e^{u}=8π\sum_{k=0}^{3}n_{k}δ_{\frac{ω_{k}}{2}}% +4π\left( δ_{p}+δ_{-p}\right) \quad \text{ on }\;E_τ:…

math.AP2025

Generic non-degeneracy of critical points of multiple Green functions on torus and applications to curvature equations

Zhijie Chen, Erjuan Fu, Chang-Shou Lin

Let $E_{τ} := C / (Z + Z τ)$ with $Im τ > 0$ be a flat torus and $G (z; τ)$ be the Green function on $E_{τ}$ with the singularity at $0$ . Consider the mul…

math.CA2024

Monodromy of generalized Lame equations with Darboux-Treibich-Verdier potentials: A universal law

Zhijie Chen, Chang-Shou Lin

The Darboux-Treibich-Verdier (DTV) potential $\sum_{k = 0}^{3} n_{k} (n_{k} + 1) ℘ (z + \frac{ω _{k}}{2}; τ)$ is well-known as doubly-periodic solutions of the stationary KdV hierarchy (Tr…