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:…