Complex Monge-Ampére equations on compact Hermitian manifolds.

We discuss a new approach to the uniform Linfty bound for solutions to complex Monge-Ampére equations on compact manifolds. Our method applies in degenerate contexts when the reference form is semi-positive and big, allowing to obtain bounded solutions when the right-hand side is in L^p for some p > 1. This is a joint work with Vincent Guedj.