scholarly journals Plurisubharmonic functions and Monge-Ampère operators on complex varieties in bounded domains of Cn

2021 ◽  
pp. 125477
Author(s):  
Nguyen Quang Dieu ◽  
Tang Van Long
Keyword(s):  
Bounded Domains ◽  
Plurisubharmonic Functions ◽  
Complex Varieties ◽  
Monge Ampere

scholarly journals Approximation of plurisubharmonic functions on complex varieties

2017 ◽  
Vol 28 (14) ◽  
pp. 1750107
Author(s):  
Nguyen Quang Dieu ◽  
Tang Van Long ◽  
Sanphet Ounheuan
Keyword(s):  
Continuous Function ◽  
Bounded Domain ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Plurisubharmonic Functions ◽  
Complex Variety ◽  
Complex Varieties

Let [Formula: see text] be a complex variety in a bounded domain [Formula: see text] in [Formula: see text]. We are interested in finding sufficient conditions on [Formula: see text] so that plurisubharmonic functions which are bounded from above on [Formula: see text] can be approximated from above by continuous functions on [Formula: see text] and plurisubharmonic on [Formula: see text] Next, we discuss the possibility to extend a given real valued continuous function on [Formula: see text] to a maximal plurisubharmonic on [Formula: see text] which is continuous up to the boundary.

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.

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