Related papers: A comparison principle for bounded plurisubharmoni…
In this paper, we introduce a notion of singularity comparison for plurisubharmonic functions based on the Bedford--Taylor capacity. We establish comparison principles for the complex Monge--Amp\`ere operator on pluripolar sets in the…
We prove a comparison principle for the pluripotential complex Monge-Amp\`ere flows for the right-hand side of the form $dt \wedge d\mu$ where $d\mu$ is dominated by a Monge-Amp\`ere measure of a bounded plurisubharmonic function. As a…
We prove one decomposition theorem of complex Monge-Ampere measures of plurisubharmonic functions in connection with their pluripolar sets.
The purpose of this paper is to study convergence of Monge-Ampere measures associated to sequences of plurisubharmonic functions defined on a hyperconvex subset of ${\mathbb C^n}$.
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-Amp\`ere equations.
The aim of this paper is to give a new proof of the complete characterization of measures for which there exist a solution of the Dirichlet problem for the complex Monge-Ampere operator in the set of plurisubharmonic functions with finite…
We study swept-out Monge-Ampere measures of plurisubharmonic functions and boundary values related to these measures.
We give a version of the comparison principle from pluripotential theory where the Monge-Amp\`ere measure is replaced by the Bergman kernel and use it to derive a maximum principle
In this paper, we prove a Moser-Trudinger type inequality for pluri-subharmonic functions vanishing on the boundary. Our proof uses a descent gradient flow for the complex Monge-Ampere functional.
We will define the Monge-Amp\`ere operator on finite (weakly) plurifinely plurisubharmonic functions in plurifinely open sets in complex n-space and show that it defines a positive measure. Ingredients of the proof include a direct proof…
The main goal of this article is to find, following the approach given in [Ce1] and [Ce2], the largest possible sub-class of plurisubharmornic functions on a complex variety on which the complex Monge-Amp\`ere operator can be reasonably…
We prove some results which give sufficient conditions so that pointwise approximation of negative plurisubharmonic functions on complex varieties by continuous plurisubharmonic ones is possible.
In this article we will first prove a result about convergence in capacity. Using the achieved result we will obtain a general decompositon theorem for complex Monge-Ampere measues which will be used to prove a comparison principle for the…
This paper studies the complex Monge-Amp\`ere equations for $\mathcal F$-plurisubharmonic functions in bounded $\mathcal F$-hyperconvex domains. We give sufficient conditions for this equation to solve for measures with a singular part.
We study classes of convex functions on balanced polyhedral spaces and establish various structural properties, including a compactness theorem for polyhedrally plurisubharmonic functions. Using tropical intersection theory, we construct…
In this paper, we prove a Moser-Trudinger type inequality for pluri-subharmonic functions vanishing on the boundary. Our proof uses a descent gradient flow for the complex Monge-Ampere functional.
The aim of the paper is to investigate the structure of plurifinely open sets. As an application, we will prove an equality on complex Monge-Amp\`ere measures in plurifinely open sets.
We give a sufficient condition on a sequence of uniformly bounded $\omega$-plurisubharmonic functions, $\omega$ being a Hermitian metric, for which the sequence of associated Monge-Amp\`ere measures converges weakly. This criterion can be…
We show that the spaces of $A$-$m$-subharmonic and $B$-$m$-subharmonic functions differ in sufficently high dimensions. We also prove that the Monge-Amp\`ere type operator $\mathcal M_m$ associated to the space of $m$-plurisubharmonic…
Let $w_0$ be a bounded, $C^3$, strictly plurisubharmonic function defined on $B_1\subset \mathbb{C}^n$. Then $w_0$ has a neighborhood in $L^{\infty}(B_1)$. Suppose that we have a function $\phi$ in this neighborhood with $1-\epsilon \le…