Chang-Shou Lin

collaborators

4 papers

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…