Non-existence of solutions for a mean field equation on flat tori at critical parameter $16\pi$

Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin

It is known from \cite{LW} that the solvability of the mean field equation $\Delta u+e^u=8n\pi {\delta }_0$ with $n\in {\mathbb{N}}_{\ge 1}$ on a flat torus $E_{\tau }$ essentially depends on the geome…