Relative pluripotential theory on compact Kähler manifolds

Abstract

Given a compact Kähler manifold, we survey the study of complex Monge-Ampère 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-Ampère operator.

v2. no major changes, many imprecisions fixed

References in corpus (4)

• Integration by parts formula for non-pluripolar product
• Quasi-plurisubharmonic envelopes 1: Uniform estimates on Kähler manifolds
• Quantitative stability for the complex Monge-Ampere equations
• A transcendental approach to non-Archimedean metrics of pseudoeffective classes

Cited by in corpus (1)

• Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting