turkmath.org

In this talk we will consider two different classes of quasi-plurisubharmonic functions on compact K¨ahler manifolds, namely classical finite energy classes and the Choquet-Monge-Amp`ere classes. These classes play an important role in the analysis of the Complex Monge-Amp`ere operator on compact K¨ahler manifolds. We will first characterize these classes through their energy levels and then we will compare them. We will see that over different singularity types, the comparison between these classes yields totally different characteristics. This is joint work with Vincent Guedj (IMT) and Ahmed Zeriahi (IMT).