Abstract: Liouville equations are of elliptic type and involve exponential nonlinear terms. In this talk, we will talk about the blow-up analysis of Liouville type equations on cylinder, and then give the energy quantization for Liouville equations with conical singularities. Next, we consider the equation with cusp singularity in a punctured disc. In this situation, we will talk about the blow-up and energy concentration phenomenon. Finally, we consider mean field equations on degenerating Riemannian surfaces. In this case, the energy of the solution near the degenerate point is studied and we obtain the energy identity.
