Related papers: Local inequalities for plurisubharmonic functions

In this paper we present necessary and sufficient conditions (in terms of {\L}ojasiewicz inequalities) for the stability of local minimum points in smooth unconstrained optimization. In particular, we derive a sufficient condition for which…

Let $\Omega$ be a strongly pseudoconvex domain. We introduce the Mabuchi space of strongly plurisubharmonic functions in $\Omega$. We study metric properties of this space using Mabuchi geodesics and establish regularity properties of the…

Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…

The aim of this work is to expose some asymptotic series associated to some expressions involving the volume of the n-dimensional unit ball. All proofs and the methods used for improving the classical inequalities announced in the final…

Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomials. We introduce various anisotropic model classes based on…

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…

In this note we derive a sharp concentration inequality for the supremum of a smooth random field over a finite dimensional set. It is shown that this supremum can be bounded with high probability by the value of the field at some…

In this paper, we give a new generalization of the Bohr inequality in refined form both for bounded analytic functions, and for sense-preserving harmonic functions with analytic part being bounded.

We introduce a quantity which measures the singularity of a plurisubharmonic function f relative to another plurisubharmonic function g, at a point a. This quantity, which we denote by $\nu_{a,g}(f)$, can be seen as a generalization of the…

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.

It is shown that harmonic functions on some subsets, subharmonic and coinciding everywhere outside of these sets, actually coincide everywhere.

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 present a new proof of Thurston's theorem that the unit ball of a seminorm on $\mathbf{R}^d$ taking integer values on $\mathbf{Z}^d$ is a polyhedra defined by finitely many inequalities with integer coefficients.

In this survey we consider polynomial optimization problems, asking to minimize a polynomial function over a compact semialgebraic set, defined by polynomial inequalities. This models a great variety of (in general, nonlinear nonconvex)…

We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of a…

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

This is a survey on eigenfunctions of the Laplacian on Riemannian manifolds (mainly compact and without boundary). We discuss both local results obtained by analyzing eigenfunctions on small balls, and global results obtained by wave…

We establish the equivalence of the analytic and probabilistic notions of subharmonicity in the framework of general symmetric Hunt processes on locally compact separable metric spaces, extending an earlier work of the first named author on…

The present paper contains some investigations about a uniform variant of the notion of metric hemiregularity, the latter being a less explored property obtained by weakening metric regularity. The introduction of such a quantitative…

The main goal of this paper is to construct an algebraic analogue of quasi-plurisubharmonic function (qpsh for short) from complex analysis and geometry. We define a notion of qpsh function on a valuation space associated to a quite general…