The General Definition of the Complex Monge-Ampère Operator on Compact Kähler Manifolds

2007/05/15 by Yang Xing, Xing, Yang
Mathematics · #32Q15 #32W20 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0705.2099

openalex publication_date 2007/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a wide subclass \cal F(X,ω) of quasi-plurisubharmonic functions in a compact Kähler manifold, on which the complex Monge-Ampère operator is well-defined and the convergence theorem is valid. We also prove that \cal F(X,ω) is a convex cone and includes all quasi-plurisubharmonic functions which are in the Cegrell class.

Related

• Monge-Ampère operators on compact Kähler manifolds
• Continuity of the Complex Monge-Ampere Operator on Compact Kahler Manifolds
• Domains of definition of Monge-Ampère operators on compact Kähler manifolds
• Characterizing the range of the complex Monge-Ampère operator
• The weigthed Monge-Ampère energy of quasiplurisubharmonic functions