Zhen Song

Sharp criteria for the existence of solutions to curvature equations with two singular sources on rectangular torus

We study the following curvature equation with two singular sources on a flat torus $$ \Delta u+e^u=8\pi(\delta_p+\delta_{-p})\quad\text{on } E_\tau:=\mathbb{C}/(\mathbb{Z}+\mathbb{Z}\tau), $$ where $\delta_p$ denotes the Dirac measure at $p$. The case $\wp'(2p)=0$ was solved by Kuo (J. Differential Geom. 2026). In thi...