Characterizing the range of the complex Monge-Ampère operator

2024/12/04 by Liu, Songchen
#32Q15 #32U15 #32W20 #35D30 #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.03445

Abstract

In this note, we solve the complex Monge-Ampère equation for measures with a pluripolar part in compact Kähler manifolds. 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.

Related

• Continuity of the Complex Monge-Ampere Operator on Compact Kahler Manifolds
• Monge-Ampère operators on compact Kähler manifolds
• Monge-Ampère measures of bounded potentials
• Complex Monge-Ampère equations for plurifinely plurisubharmonic functions
• The Range of the Monge-Ampère operator (ω+ dd^c .)ⁿ in bounded domains