Explicit Solutions to the mean field equations on hyperelliptic curves   of genus two
  Let $X$be a complex hyperelliptic curve of genus two equipped with the canonical metric $ds^2$. We study mean field equations on complex hyperelliptic curves and show that the Gaussian curvature function of $(X,ds^2)$ determines an explicit solution to a mean field equation. 
Jia-Ming (Frank) Liou
math.DG math.AG math.AP