From the 1 of 4 linked papers with an AI index.
4 papers
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…
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}δ_{\frac{Ï_{k}}{2}}% +4Ï\left( δ_{p}+δ_{-p}\right) \quad \text{ on…
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 with be a flat torus and be the Green function on with the singularity at . Consider th…
Co-Axial Metrics on the Sphere and Algebraic Numbers
Zhijie Chen, Chang-Shou Lin, Yifan Yang
In this paper, we consider the following curvature equation $$Îu+{\rm e}^u=4Ï\biggl((θ_0-1)δ_0+(θ_1-1)δ_1 +\sum_{j=1}^{n+m}\bigl(θ_j'-1\bigr)δ_{t_j}\biggr)\qquad \text{in}\…