Sharp nonexistence results for curvature equations with four singular sources on rectangular tori

Zhijie Chen, Chang-Shou Lin

In this paper, we prove that there are no solutions for the curvature equation \[ Δu+e^{u}=8πnδ_{0}\text{ on }E_τ, \quad n\in\mathbb{N}, \] where $E_{\tau }$ is a flat rectangular torus…