Monge–Ampère measures of maximal subextensions of plurisubharmonic functions with given boundary values

2014 ◽  
Vol 60 (3) ◽  
pp. 429-435 ◽  
Author(s):  
Nguyen Xuan Hong
Keyword(s):  
Boundary Values ◽  
Plurisubharmonic Functions ◽  
Monge Ampere

Convergence in capacity of plurisubharmonic functions with given boundary values

2017 ◽  
Vol 28 (03) ◽  
pp. 1750018 ◽  
Author(s):  
Nguyen Xuan Hong ◽  
Nguyen Van Trao ◽  
Tran Van Thuy
Keyword(s):  
Boundary Values ◽  
Plurisubharmonic Functions ◽  
Monge Ampere ◽  
Stability Results ◽  
Convergence In Capacity

In this paper, we study the convergence in the capacity of sequence of plurisubharmonic functions. As an application, we prove stability results for solutions of the complex Monge–Ampère equations.

APPROXIMATION OF NEGATIVE PLURISUBHARMONIC FUNCTIONS WITH GIVEN BOUNDARY VALUES

2010 ◽  
Vol 21 (09) ◽  
pp. 1135-1145 ◽  
Author(s):  
LISA HED
Keyword(s):  
Plurisubharmonic Function ◽  
Boundary Values ◽  
Plurisubharmonic Functions

In this paper, we study the approximation of negative plurisubharmonic functions with given boundary values. We want to approximate a plurisubharmonic function by an increasing sequence of plurisubharmonic functions defined on strictly larger domains.

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.

Sign in / Sign up

Export Citation Format

Share Document