scholarly journals On a convex level set of a plurisubharmonic function and the support of the Monge–Ampère current

2018 ◽  
Vol 121 (3) ◽  
pp. 251-262 ◽  
Author(s):  
Yusaku Tiba
Keyword(s):  
Level Set ◽  
Plurisubharmonic Function ◽  
Monge Ampere

scholarly journals On Construction of Positive Closed Currents with Prescribed Lelong Numbers

2020 ◽  
pp. 331-341
Author(s):  
Hedi Khedhiri
Keyword(s):  
Growth Condition ◽  
Compact Subset ◽  
Level Set ◽  
Level Sets ◽  
Plurisubharmonic Function ◽  
Lelong Numbers ◽  
The Family ◽  
Closed Current ◽  
Upper Level ◽  
Positive Closed Current

We establish that a sequence (Xk)k∈N of analytic subsets of a domain Ω in Cn, purely dimensioned, can be released as the family of upper-level sets for the Lelong numbers of some positive closed current. This holds whenever the sequence (Xk)k∈N satisfies, for any compact subset L of Ω, the growth condition Σ k∈N Ck mes(Xk ∩ L) < ∞. More precisely, we built a positive closed current Θ of bidimension (p, p) on Ω, such that the generic Lelong number mXk of Θ along each Xk satisfies mXk = Ck. In particular, we prove the existence of a plurisubharmonic function v on Ω such that, each Xk is contained in the upper-level set ECk (ddcv)

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.

scholarly journals Weak solution of parabolic complex Monge–Ampère equation II

2016 ◽  
Vol 27 (12) ◽  
pp. 1650098
Author(s):  
Do Hoang Son
Keyword(s):  
Boundary Condition ◽  
Weak Solution ◽  
Pseudoconvex Domain ◽  
Plurisubharmonic Function ◽  
Initial Condition ◽  
Strictly Pseudoconvex Domain ◽  
Monge Ampere

We study the equation [Formula: see text] in [Formula: see text], where [Formula: see text] and [Formula: see text] is a bounded strictly pseudoconvex domain in [Formula: see text], with the boundary condition [Formula: see text] and the initial condition [Formula: see text]. In this paper, we consider the case, where [Formula: see text] is smooth and [Formula: see text] is an arbitrary plurisubharmonic function in a neighborhood of [Formula: see text] satisfying [Formula: see text].

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