Related papers: A comparison principle for bounded plurisubharmoni…

Let $X$ be a compact K\"ahler manifold and let $\mu$ be a non-pluripolar measure on $X$. We give a necessary and sufficient condition for $\mu$ so that the complex Monge-Amp\`ere equation (in a K\"ahler class in $X$) having $\mu$ as the…

An analytic pair of dimension n and center V is a pair (V, M) where M is a complex manifold of (complex) dimension n and V is a closed totally real analytic submanifold of dimension n. To an analytic pair (V, M) we associate the class of…

A notion of local indicator for a plurisubharmonic function is introduced. The indicator is a certain plurisubharmonic function in the unit polydisc, which controls the behavior of the considered function near a fixed point of its…

In this article we address the question whether the complex Monge-Amp\`{e}re equation is solvable for measures with large singular part. We prove that under some conditions there are no solution when the right-hand side is carried by a…

We prove several results showing that plurisubharmonic functions with various bounds on their Monge-Ampere masses on a bounded hyperconvex domain always admit global plurisubharmonic subextension with logarithmic growth at infinity.

This work extends the Mond-Pecaric method to functions with multiple operators as arguments by providing arbitrarily close approximations of the original functions. Instead of using linear functions to establish lower and upper bounds for…

In \cite{GL21a} we have developed a new approach to $L^{\infty}$-a priori estimates for degenerate complex Monge-Amp\`ere equations, when the reference form is closed. This simplifying assumption was used to ensure the constancy of the…

Two properties of plurisubharmonic functions are proven. The first result is a Skoda type integrability theorem with respect to a Monge-Amp\`ere mass with H\"older continuous potential. The second one says that locally, a p.s.h. function is…

We study a Monge-Amp\`ere type equation in the class of $p$-plurisubharmonic functions and establish first and second order interior estimates. As an application of these we show that $p$-plurisubharmonic functions with constant operator…

We prove that the composition of a quasi-nearly subharmonic function and a quasiregular mappings of bounded multiplicity is quasi-nearly subharmonic. Also, we prove that if $u\circ f$ is quasi-nearly subharmonic for all quasi-nearly…

We prove estimates, similar in form to the classical Aleksandrov estimates, for a Monge-Ampere type operator on the Heisenberg group. A notion of normal mapping does not seem to be available in this context and the method of proof uses…

We prove a multivariable approximate Carleman theorem on the determination of complex measures on ${\mathbb{R}}^n$ and ${\mathbb{R}}^n_+$ by their moments. This is achieved by means of a multivariable Denjoy--Carleman maximum principle for…

In this paper, we consider the Monge-Amp\`{e}re type equations on compact almost Hermitian manifolds. We derive $C^{\infty}$ a priori estimates under the existence of an admissible $\mathcal{C}$-subsolution. Finally, we obtain an existence…

We first study subextensions of m-subharmonic functions in weighted energy classes with given boundary values. The results are used to approximate an m-subharmonic function in weighted energy classes with given boundary values by an…

Let $u$ be a maximal plurisubharmonic function in a domain $\Omega\subset\mathbb{C}^n$ ($n\geq 2$). It is classical that, for any $U\Subset\Omega$, there exists a sequence of bounded plurisubharmonic functions $PSH(U)\ni u_j\searrow u$…

The main objective of this paper is to prove a new inequality for plurisubharmonic functions estimating their supremum over a ball by their supremum over a measurable subset of the ball. We apply this result to study local properties of…

We prove a comparison principle for positive supersolutions and subsolutions to the Lane-Emden equation for the $p-$Laplacian, with subhomogeneous power in the right-hand side. The proof uses variational tools and the result applies with no…

We characterize the class of probability measures on a compact Kahler manifold such that the associated Monge-Amp\`ere equation has a solution of finite pluricomplex energy. Our results are also valid in the big cohomology class setting.

We prove general results about separation and weak$^\#$-convergence of boundedly finite measures on separable metric spaces and Souslin spaces. More precisely, we consider an algebra of bounded real-valued, or more generally a $*$-algebra…

Let $(X, \omega)$ be a compact K\"ahler manifold of complex dimension n and $\theta$ be a smooth closed real $(1,1)$-form on $X$ such that its cohomology class $\{ \theta \}\in H^{1,1}(X, \mathbb{R})$ is pseudoeffective. Let $\varphi$ be a…