Related papers: Differential tests for plurisubharmonic functions …

The aim of this paper is to present an original approach that takes advantage from the geometric features of strictly convex functions to tackle the problem of finding the minimum from another perspective. The general idea is that near the…

We study the complex Monge-Amp\`ere operator in bounded hyperconvex domains of $\C^n$. We introduce a scale of classes of weakly singular plurisubharmonic functions : these are functions of finite weighted Monge-Amp\`ere energy. They…

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.

Based on two independent samples X_1,...,X_m and X_{m+1},...,X_n drawn from multivariate distributions with unknown Lebesgue densities p and q respectively, we propose an exact multiple test in order to identify simultaneously regions of…

In the present paper we prove several results concerning the existence of low-discrepancy point sets with respect to an arbitrary non-uniform measure $\mu$ on the $d$-dimensional unit cube. We improve a theorem of Beck, by showing that for…

Let $M$ be a complex manifold and $PSH^{cb}(M)$ be the space of bounded continuous plurisubharmonic functions on $M$. In this paper we study when functions from $PSH^{cb}(M)$ separate points. Our main results show that this property is…

Replying to three questions posed by N. Shcherbina, we show that a compact psudoconcave set can have the core smaller than itself, that the core of a compact set must be pseudoconcave, and that it can be decomposed into compact…

Let $D$ be a domain in a finite-dimensional Euclidean space, and $H$ be a convex subcone in the convex cone of all subharmonic functions on $D$. We obtain a criterion for the existence of a lower envelope from $H$ for an arbitrary function…

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.

We initiate the study of fine $p$-(super)minimizers, associated with $p$-harmonic functions, on finely open sets in metric spaces, where $1 < p < \infty$. After having developed their basic theory, we obtain the $p$-fine continuity of the…

While discrete harmonic functions have been objects of interest for quite some time, this is not the case for discrete polyharmonic functions, as appear for instance in the asymptotics of path counting problems. In this article, a novel…

The purpose of this article is to study the (residual) Monge-Amp\`{e}re mass of a plurisubharmonic function with an isolated unbounded locus. A general decomposition formula is obtained under the Sasakian structure of the unit sphere. In…

We extend the notion of quasibounded harmonic functions to the plurisubharmonic setting. As an application, using the theory of Jensen measures, we show that certain generalized Dirichlet problems with unbounded boundary data admit unique…

Let $(X,\omega)$ be a compact Hermitian manifold and let $\{\beta\}\in H^{1,1}(X,\mathbb R)$ be a real $(1,1)$-class with a smooth representative $\beta$, such that $\int_X\beta^n>0$. Assume that there is a bounded $\beta$-plurisubharmonic…

First we extend the theory of subharmonic functions on smooth strictly $k$-analytic curves from Thuillier's thesis to the case of possibly singular analytic curves over a non-archimedean field. Classically psh functions are then defined as…

Given a bounded finely open set $V$ and a function $f$ on the fine boundary of $V$, we introduce four types of upper Perron solutions to the nonlinear Dirichlet problem for $p$-energy minimizers, $1<p<\infty$, with $f$ as boundary data.…

In this paper, we derive mutual information based upper and lower bounds on the number of nonadaptive group tests required to identify a given number of "non defective" items from a large population containing a small number of "defective"…

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 study swept-out Monge-Ampere measures of plurisubharmonic functions and boundary values related to these measures.

Let $u$ and $v$ be two plurisubharmonic functions in the domain of definition of the Monge-Amp\`ere operator on a domain $\Omega\subset {\bf C}^n$. We prove that if $u=v$ on a plurifinely open set $U\subset \Omega$ that is Borel measurable,…