Complex Monge-Ampère equations on quasi-projective varieties

2014/01/24 by Di Nezza, Eleonora, Lu, Chinh H.
#Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1401.6398

Abstract

We introduce generalized Monge-Ampère capacities and use these to study complex Monge-Ampère equations whose right-hand side is smooth outside a divisor. We prove, in many cases, that there exists a unique normalized solution which is smooth outside the divisor.

Related

• L¹-Stability for complex Monge-Ampère equations
• Generalized Monge-Ampère capacities
• Auxiliary Monge-Ampere equations in geometric analysis
• The Monge-Ampère equation on almost complex manifolds
• The boundary case for complex Monge-Ampère type equations