The complex Monge-Ampère equation

Abstract

Chapter 1 1.1. Introduction 1.2. Preliminaries Chapter 2 2.1. The complex Monge~Amp~re equation on a compact Kiihler manifold. Results 2.2. Weak solutions to the Monge-Amp~re equation 2.3. L~-estimates for the solution 2.4. Continuity of the solution 2.5. Functions satisfying condition (A) 2.6. Solutions to the Monge-Amp~re equation belonging to L+ Chapter 3 3.1. The complex Monge-Amp~re equation in a strictly pseudoconvex domain. Results 3.2. Preliminaries for the proofs of Theorems A and C 3.3. Proof of Theorem A 3.4. Proof of Theorem C 3.5. Measures admitting solutions to the Monge-Amp~re equation