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 $$Δu+{\rm e}^u=4π\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}\ \mathbb…