Relative pluripotential theory on compact K\"ahler manifolds

Abstract

Given a compact K\"ahler manifold, we survey the study of complex Monge-Amp\`ere type equations with prescribed singularity type, developed by the authors in a series of papers. In addition, we give a general answer to a question of Guedj--Zeriahi about the finite energy range of the complex Monge-Amp\`ere operator.