Characterizing the range of the complex Monge–Ampère operator
Abstract
In this paper, we solve the complex Monge–Ampère equation for measures with a pluripolar part in the Cegrell class on compact Kähler manifolds, and require that the pluripolar part is solvable within this framework. This result generalizes the classical results obtained by Cegrell in bounded hyperconvex domains. We also discuss the properties of the complex Monge-Ampère operator in some special cases.
Fields of Study & Subjects
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- International Journal of Mathematics
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 37
- Issue
- 09
- Publication date
- 17 April 2026
- Language
- EN