Related papers: Continuity Properties of Finely Plurisubharmonic F…

A weak and a strong concept of plurifinely plurisubharmonic and plurifinely holomorphic functions are introduced. Strong will imply weak. The weak concept is studied further. A function f is weakly plurifinely plurisubharmonic if and only…

We prove that the graph of a continuous function $f$, defined on a domain of ${\mathbb C}^n$, is pluripolar if and only if $f$ is holomorphic.

In this paper, we prove that a continuous $\mathcal F$-plurisubharmonic functions defined in an $\mathcal F$-open set in $\mathbb C^n$ is $\mathcal F$-maximal if and only if it is $\mathcal F$-locally $\mathcal F$-maximal.

In this note we study the plurifinely locally maximal plurifinely plurisubharmonic functions and improve some known results on these functions. We prove in particular that any locally bounded plurifinely locally maximal plurifinely…

We prove that the set of points where a subharmonic function fails to be continuous is polar.

Examples by Poletsky and the author and by Zwonek show the existence nowhere extendable holomorphic functions with the property that the pluripolar hull of their graphs is much larger than the graph of the respective functions and contains…

Let A be a closed polar subset of a domain D in the complex plane C. We give a complete description of the pluripolar hull in D X C of the graph of a holomorphic function defined on D A. To achieve this, we prove for pluriharmonic measure…

We prove that the image of a finely holomorphic map on a fine domain in $\mathbb{C}$ is pluripolar subset of $\mathbb{C}^{n}$. We also discuss the relationship between pluripolar hulls and finely holomorphic function.

In this paper, we combine tools from pluripotential theory and commutative algebra to study singularity invariants of plurisubharmonic functions. We establish several relationships between the singularity invariants of 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 study boundary properties of plurisubharmonic functions near real submanifolds of almost complex manifolds.

This is a survey of results, both classical and recent, on behaviour of plurisubharmonic functions near their $-\infty$-points, together with the related topics for positive closed currents.

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.…

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 give characterizations of (quasi-)plurisubharmonic functions in terms of $L^p$-estimates of $\bar\partial$ and $L^p$-extensions of holomorphic functions.

We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of…

Recently the authors showed that there is a robust potential theory attached to any calibrated manifold (X,\phi). In particular, on X there exist \phi-plurisubharmonic functions, \phi-convex domains, \phi-convex boundaries, etc., all…

In this paper, we first show that a union of upper-level sets associated to fibrewise Lelong numbers of plurisubharmonic functions is in general a pluripolar subset. Then we obtain analyticity theorems for a union of sub-level sets…

We introduce multi-split continuous functions between topological spaces, a weaker form of continuity that generalizes split continuity while being stable under compositions. We will define the associated star multifunction and…

We study properties of relative types of plurisubharmonic functions with respect to maximal plurisubharmonic weights. It is shown that they give a general form for upper semicontinuous, tropically additive functionals on plurisubharmonic…