Related papers: Plurisubharmonic functions and nef classes on comp…
We study seminormalization of affine complex varieties. We show that polynomials on the seminormalization correspond to the rational functions which are continuous for the Euclidean topology. We further study this type of functions which…
We study functions defined on a closed segment of the real line that belong to the class of Gonchar. We show that the graphs of such functions are pluripolar. We also discuss the generalizations of our result to functions defined on a…
Morse functions are important objects and tools in understanding topologies of manifolds since the 20th century. Their classification has been natural and difficult problems, and surprisingly, this is recently developing. Since the 2010's,…
We study various regularization operators on plurisubharmonic functions that preserve Lelong classes with growth given by certain compact convex sets. The purpose is to show that the weighted Siciak-Zakharyuta functions associated with…
We undertake a preliminary step towards studying non-Archimedean pluripotential theory on polarized affine cones over a trivially valued field. We study plurisubharmonic functions and the Monge--Amp\`ere operator defined on the finite…
A fundamental construction in formal language theory is the Myhill-Nerode congruence on words, whose finitedness characterizes regular language. This construction was generalized to functions from $\Sigma^*$ to $\mathbb{Z}$ by Colcombet,…
Let X be a complex manifold of dimension at least 2 which has an exhaustion function whose Levi form has at each point at least 2 positive eigenvalues. We prove that there are proper holomorphic discs in X through any given point
In this contribution we announce a complete classification and new exotic phenomena of the meromorphic structure of $\z$-functions associated to conic manifolds proved in \cite{KLP1}. In particular, we show that the meromorphic extensions…
A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…
We prove that square integrable holomorphic functions (with respect to a plurisubharmonic weight) can be extended in a square integrable manner from certain singular hypersurfaces (which include uniformly flat, normal crossing divisors) to…
The main purpose of this paper is to introduce and study the notion of plurifinely-maximal plurifinely plurisubharmonic functions, which extends the notion of maximal plurisubharmonic functions on a Euclidean domain to a plurifine domain 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…
In this paper, we introduce the notion of strong locally irreducible complex spaces $\widetilde{X}$. Based on this notion we prove the equality $\bar{\nu}_{\varphi}(x)=$ mult$(\widetilde{X},x). \nu_{\varphi}(x)$ for all $x\in…
We generalize the Poletsky disc envelope formula for the function $\sup \{u \in \PSH(X,\omega) ; u\leq \phi\}$ on any complex manifold $X$ to the case where the real (1,1)-current $\omega=\omega_1-\omega_2$ is the difference of two positive…
In the first part of this paper, we study the properties of some particular plurisubharmonic functions, namely the toric ones. The main result of this part is a precise description of their multiplier ideal sheaves, which generalizes the…
In the present paper, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of orthogonal polynomials are provided based on 2-parameters weight functions. Such classes englobe the well…
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.
We prove a Noether--Lefschetz-type result for certain linear systems on a projective threefold with isolated singularities.
First, we classify proper biharmonic Hopf real hypersurfaces in $\mathbb{C}P^2$. Next, we classify proper biharmonic real hypersurfaces with two distinct principal curvatures in $\mathbb{C}P^n$, where $n\geq 2$. Finally, we prove that…
It is shown that most of the well-known basic results for Sobolev-Slobodeckii and Bessel potential spaces, known to hold on bounded smooth domains in $\mathbb{R}^n$, continue to be valid on a wide class of Riemannian manifolds with…