Chang-Shou Lin

works on

critical points 1 curvature equation 1 flat torus 1 green function 1 rhombus torus 1

From the 1 of 7 linked papers with an AI index.

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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_{I ¨} $ with $4 I ¨ $ conic angle at each half period point\, $I ¨ _{k} / 2, k = 0, 1, 2, 3$ \, is equivalent to classify solutions of the followin…

math.AP2026

Geometric analysis on rhombus torus: Green function with two singularities

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

The paper studies how the geometry of a rhombus-shaped flat torus and the positions of two singularities affect the critical points of a symmetrized Green function, and uses this t…

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 $E_{I ¨} = C / (Z + Z I ¨ )$ with the singularity at $0$ . Lin and Wang (Ann. Math. 2010) proved that $G (z)$ has ei…

math.AP2025

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

Zhijie Chen, Erjuan Fu, Chang-Shou Lin

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

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 \[Îu+e^{u}=8Ï\sum_{k=0}^{3}n_{k}Î´_{\frac{Ï_{k}}{2}}% +4Ï\left( Î´_{p}+Î´_{-p}\right) \quad \text{ on…

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