Abstract
Partial Differential Equations on manifolds areusually treated with classical analytical techni-ques. The combination of those with geometricalstructures of the manifold may yield improvementsor even the development of new strategies toapproach thsese equations. The method we have been using studies a non-linear elliptic equationof the type $\Delta u +f(x)exp(2u)-\lambda=0$ ona Riemann Su…