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.

THE DIRICHLET PROBLEM FOR MAXIMAL PLURISUBHARMONIC FUNCTIONS ON ANALYTIC VARIETIES IN ℂn

2009 ◽  
Vol 20 (04) ◽  
pp. 521-528 ◽  
Author(s):  
FRANK WIKSTRÖM
Keyword(s):  
Dirichlet Problem ◽  
Continuous Function ◽  
Plurisubharmonic Function ◽  
Boundary Values ◽  
Regular Domain ◽  
Analytic Variety ◽  
Plurisubharmonic Functions ◽  
Analytic Varieties

Let Ω be a B-regular domain in ℂn and let V be a locally irreducible analytic variety in Ω. Given a continuous function [Formula: see text], we prove that there is a unique maximal plurisubharmonic function u on V with boundary values given by ϕ and furthermore that u is continuous on [Formula: see text].

scholarly journals Extremal $\omega$-plurisubharmonic functions as envelopes of disc functionals: generalization and applications to the local theory

2012 ◽  
Vol 111 (2) ◽  
pp. 296
Author(s):  
Benedikt Steinar Magnússon
Keyword(s):  
Complex Manifold ◽  
Plurisubharmonic Function ◽  
Local Theory ◽  
Semicontinuous Function ◽  
Plurisubharmonic Functions ◽  
The Real ◽  
Upper Semicontinuous ◽  
The Difference ◽  
Upper Semicontinuous Function

We generalize the Poletsky disc envelope formula for the function $\sup \{u\in \mathcal{PSH}(X,\omega); u\leq \phi\}$ on any complex manifold $X$ to the case where the real $(1,1)$-current $\omega=\omega_1-\omega_2$ is the difference of two positive closed $(1,1)$-currents and $\varphi$ is the difference of an $\omega_1$-upper semicontinuous function and a plurisubharmonic function.

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.

scholarly journals A cup product lemma for continuous plurisubharmonic functions

2018 ◽  
Vol 10 (02) ◽  
pp. 263-287
Author(s):  
Terrence Napier ◽  
Mohan Ramachandran
Keyword(s):  
Plurisubharmonic Function ◽  
Kähler Manifold ◽  
Analytic Set ◽  
Plurisubharmonic Functions ◽  
Structure Sheaf ◽  
Compactly Supported ◽  
Cup Product ◽  
Kahler Manifold ◽  
Complete Kähler Manifold

A version of Gromov’s cup product lemma in which one factor is the (1, 0)-part of the differential of a continuous plurisubharmonic function is obtained. As an application, it is shown that a connected noncompact complete Kähler manifold that has exactly one end and admits a continuous plurisubharmonic function that is strictly plurisubharmonic along some germ of a [Formula: see text]-dimensional complex analytic set at some point has the Bochner–Hartogs property; that is, the first compactly supported cohomology with values in the structure sheaf vanishes.

Complex Monge-Ampère Measures of Plurisubharmonic Functions with Bounded Values Near the Boundary

2000 ◽  
Vol 52 (5) ◽  
pp. 1085-1100 ◽  
Author(s):  
Yang Xing
Keyword(s):  
Positive Measure ◽  
Plurisubharmonic Function ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Plurisubharmonic Functions ◽  
Necessary And Sufficient ◽  
Monge Ampere

AbstractWe give a characterization of bounded plurisubharmonic functions by using their complex Monge-Ampère measures. This implies a both necessary and sufficient condition for a positive measure to be complex Monge-Ampère measure of some bounded plurisubharmonic function.

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