Related papers: On compacts possessing strictly plurisubharmonic f…

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.

We prove that the maximum of two smooth strictly plurisubharmonic functions on an almost complex manifold can be uniformly approximated by smooth strictly plurisubharmonic functions.

We establish the plurisubharmonicity of the envelope of the Poisson functional on almost complex manifolds. That is, we generalize the corresponding result for complex manifolds and almost complex manifolds of complex dimension two.

This note establishes smooth approximation from above for J-plurisubharmonic functions on an almost complex manifold (X,J). The following theorem is proved. Suppose X is J-pseudoconvex, i.e., X admits a smooth strictly J-plurisubharmonic…

We introduce different classical characteristics used to regularize a subharmonic function and compare them. As an application we give a complete proof of a useful characterization of the modulus of continuity of such functions in terms of…

We provide a sufficient condition for open sets W and X such that a disc formula for the largest plurisubharmonic subextension of an upper semicontinuous function on a domain W to a complex manifold X holds.

Let $(M,\omega)$ be a Kahler manifold. An integrable function on M is called $\omega^q$-plurisubharmonic if it is subharmonic on all q-dimensional complex subvarieties. We prove that a smooth $\omega^q$-plurisubharmonic function is…

Necessary conditions for a domain $\Omega\subset \mathbb C^n$ admitting a local plurisubharmonic defining function on the boundary are given. In tandem, we give an algorithm to construct a local plurisubharmonic defining function on the…

In this note, we will present global equisingular approximations of quasi-plurisubharmonic functions with stable analytic pluripolar sets on compact complex manifolds.

We prove that a relatively compact pseudoconvex domain with smooth boundary in an almost complex manifold admits a bounded strictly plurisubharmonic exhaustion function. We use this result for the study of convexity and hyperbolicity…

We study boundary properties of plurisubharmonic functions near real submanifolds of almost complex manifolds.

We investigate the question of existence of plurisubharmonic defining functions for smoothly bounded, pseudoconvex domains in $\mathbb{C}^2$. In particular, we construct a family of simple counterexamples to the existence of…

In this paper we are concerned with the problem of local and global subextensions of (quasi-)plurisubharmonic functions from a "regular" subdomain of a compact K\"ahler manifold. We prove that a precise bound on the complex Monge-Amp\`ere…

We give some results concerning the smoothness of the image of a real-analytic submanifold in complex space under the action of a finite holomorphic mapping. For instance, if the submanifold is not contained in a proper complex subvariety,…

We study the geometric properties of complex manifolds possessing a pair of plurisubharmonic functions satisfying Monge-Amp\`ere type of condition. The results are applied to characterize complex manifolds biholomorphic to $\C^{N}$ viewed…

We show that a disc functional on a complex manifold has a plurisubharmonic envelope if all its pullbacks by holomorphic submersions from domains of holomorphy in affine space do and it is locally bounded above and upper semicontinuous in a…

In this paper we introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy many of their important properties.…

We establish plurisubharmonicity of the envelope of Lelong functional on almost complex manifolds of real dimension four, thereby we generalize the corresponding result for complex manifolds.

We establish plurisubharmonicity of the envelope of Poisson and Lelong functionals on almost complex manifolds. That is, we generalize the corresponding results for complex manifolds and almost complex manifolds of complex dimension two. We…

In this paper we solve the Dirichlet problems for different classes of plurisubharmonic functions on compact sets in $\mathbb C^n$ including continuous, pluriharmonic and maximal functions.