Related papers: Tropical analysis of plurisubharmonic singularitie…
Tropical mathematics redefines the rules of arithmetic by replacing addition with taking a maximum, and by replacing multiplication with addition. After briefly discussing a tropical version of linear algebra, we study polynomials build…
In this paper, we study the approximation of negative plurifinely plurisubharmonic function defined on a plurifinely domain by an increasing sequence of plurisubharmonic functions defined in Euclidean domains.
In this note, we will present global equisingular approximations of quasi-plurisubharmonic functions with stable analytic pluripolar sets on compact complex manifolds.
In this course of lectures we give an account of the growth theory of subharmonic functions, which is directed towards its applications to entire functions of one and several complex variables.
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.
We consider a multidimensional extremal problem formulated in terms of tropical mathematics. The problem is to minimize a nonlinear objective function, which is defined on a finite-dimensional semimodule over an idempotent semifield,…
We introduce tropical Newton-Puiseux polynomials admitting rational exponents. A resolution of a tropical hypersurface is defined by means of a tropical Newton-Puiseux polynomial. A polynomial complexity algorithm for resolubility of a…
The algebraic foundation of tropical polynomial algebra provides the framework for the geometric construction of the supplement and the reversal of tropical varieties, thereby inducing a duality of reduced tropical varieties; for classes of…
A multidimensional extremal problem in the idempotent algebra setting is considered which consists in minimizing a nonlinear functional defined on a finite-dimensional semimodule over an idempotent semifield. The problem integrates two…
This is a survey on tropical polytopes from the combinatorial point of view and with a focus on algorithms. Tropical convexity is interesting because it relates a number of combinatorial concepts including ordinary convexity, monomial…
Tropical differential equations are introduced and an algorithm is designed which tests solvability of a system of tropical linear differential equations within the complexity polynomial in the size of the system and in its coefficients.…
We study boundary properties of plurisubharmonic functions near real submanifolds of almost complex manifolds.
The purpose of this paper is to provide some properties of maximal plurisubharmonic functions in a bounded domain of \mathbb{C}^n
Tropical toric varieties are partial compactifications of finite dimensional real vector spaces associated with rational polyhedral fans. We introduce plurisubharmonic functions and a Bedford--Taylor product for Lagerberg currents on open…
Tropical Newton-Puiseux polynomials defined as piece-wise linear functions with rational coefficients at the variables, play a role of tropical algebraic functions. We provide explicit formulas for tropical Newton-Puiseux polynomials being…
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 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…
The goal of this article is to present a survey of the recent theory of plurisubharmonic functions of quaternionic variables, and its applications to theory of valuations on convex sets and HKT-geometry (HyperK\"ahler with Torsion). The…
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 consider problems of rating alternatives based on their pairwise comparison under various assumptions, including constraints on the final scores of alternatives. The problems are formulated in the framework of tropical mathematics to…