scholarly journals The Lelong number, the Monge–Ampère mass, and the Schwarz symmetrization of plurisubharmonic functions

2020 ◽  
Vol 58 (2) ◽  
pp. 369-392
Author(s):  
Long Li
Keyword(s):  
Plurisubharmonic Functions ◽  
Lelong Number ◽  
Schwarz Symmetrization ◽  
Monge Ampere

Hessian boundary measures

2019 ◽  
Vol 30 (03) ◽  
pp. 1950016
Author(s):  
Van Thien Nguyen
Keyword(s):  
Subharmonic Functions ◽  
Plurisubharmonic Functions ◽  
Lelong Number ◽  
Boundary Measure ◽  
Hessian Operator ◽  
Complex Hessian Operator ◽  
Monge Ampere

We will study certain boundary measures related to [Formula: see text]-subharmonic functions on [Formula: see text]-hyperconvex domains. These measures generalize the boundary measures studied by Wan and Wang (see [Complex Hessian operator and Lelong number for unbounded [Formula: see text]-subharmonic functions, Potential. Anal. 44(1) (2016) 53–69]). For the case of plurisubharmonic functions ([Formula: see text]) the boundary measure has been studied by Cegrell and Kemppe (see [Monge–Ampère boundary measures, Ann. Polon. Math. 96 (2009) 175–196]).

scholarly journals On Dirichlet's principle and problem

2012 ◽  
Vol 110 (2) ◽  
pp. 235 ◽  
Author(s):  
Per Åhag ◽  
Urban Cegrell ◽  
Rafal Czyz
Keyword(s):  
Dirichlet Problem ◽  
Variational Methods ◽  
Complete Characterization ◽  
Plurisubharmonic Functions ◽  
Monge Ampere

The aim of this paper is to give a new proof of the complete characterization of measures for which there exists a solution of the Dirichlet problem for the complex Monge-Ampere operator in the set of plurisubharmonic functions with finite pluricomplex energy. The proof uses variational methods.

scholarly journals On a Monge-Ampere operator for plurisubharmonic functions with analytic singularities

2019 ◽  
Vol 68 (4) ◽  
pp. 1217-1231 ◽  
Author(s):  
Matts Andersson ◽  
Zbigniew Blocki ◽  
Elizabeth Wulcan
Keyword(s):  
Plurisubharmonic Functions ◽  
Analytic Singularities ◽  
Monge Ampere

scholarly journals The General Definition of the Complex Monge–Ampère Operator on Compact Kähler Manifolds

2010 ◽  
Vol 62 (1) ◽  
pp. 218-239 ◽  
Author(s):  
Yang Xing
Keyword(s):  
Convergence Theorem ◽  
Convex Cone ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
General Definition ◽  
Kahler Manifolds ◽  
Plurisubharmonic Functions ◽  
Definition Of ◽  
Compact Kähler Manifold ◽  
Monge Ampere

AbstractWe introduce a wide subclass 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 is a convex cone and includes all quasi-plurisubharmonic functions that are in the Cegrell class.

Subextension of plurisubharmonic functions with bounded Monge–Ampère mass

2003 ◽  
Vol 336 (4) ◽  
pp. 305-308 ◽  
Author(s):  
Urban Cegrell ◽  
Ahmed Zeriahi
Keyword(s):  
Plurisubharmonic Functions ◽  
Monge Ampere
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