Entropy for Monge-Ampere Measures in the Prescribed Singularities Setting

Journal article, 2024

In this note, we generalize the notion of entropy for potentials in a relative full Monge-Ampere mass E(X, theta, phi), for a model potential phi. We then investigate stability properties of this condition with respect to blow-ups and perturbation of the cohomology class. We also prove a Moser-Trudinger type inequality with general weight and we show that functions with finite entropy lie in a relative energy class E (n/n-1) (X, theta, phi) (provided n > 1), while they have the same singularities of phi when n = 1.