An algebraic construction of a solution to the mean field equations on hyperelliptic Curves and its diabatic limit

Jia-Ming Liou, Chih-Chun Liu

In this paper, we give an algebraic construction of the solution to the following mean field equation $$\Delta \psi +e^{\psi }=4\pi \sum _{i=1}^{2g+2}{\delta }_{P_i},$$ on a genus $g\ge 2$ hyperelliptic…