Related papers: Extremal functions on moduli spaces and applicatio…
We define hypergeometric functions using intersection homology valued in a local system. Topology is emphasized; analysis enters only once, via the Hodge decomposition. By a pull-back procedure we construct special subsets S_{pi}, derived…
Motivated by long-standing conjectures on the discretization of classical inequalities in the Geometry of Numbers, we investigate a new set of parameters, which we call \emph{packing minima}, associated to a convex body $K$ and a lattice…
Submodular Functions are a special class of set functions, which generalize several information-theoretic quantities such as entropy and mutual information [1]. Submodular functions have subgradients and subdifferentials [2] and admit…
Let E be the Engel group and D be a rank 2 bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, we first prove that timelike normal extremals are locally…
We provide some new estimates for distances in harmonic function spaces of several variables related to mixed norm spaces.Some of them extend previously known assertions in this direction in the unit ball and upperhalfspace.
In this note we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution and cone-convexity, is straightforward and yields the…
We survey results concerning sharp estimates on volumes of sections and projections of certain convex bodies, mainly $\ell_p$ balls, by and onto lower dimensional subspaces. This subject emerged from geometry of numbers several decades ago…
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,…
In geometry, there are several challenging problems studying numbers associated to convex bodies. For example, the packing density problem, the kissing number problem, the covering density problem, the packing-covering constant problem,…
In this paper, we unify and improve existing results on characterizing strict and almost stricty convex functions via subdifferential mapping, Moreau envelope, and proximal mappings. In particular, it is shown that if a convex function is…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
A well known theorem of Voronoi caracterizes extreme quadratic forms and Euclidean lattices, that is those which are local maxima for the Hermite function, as perfect and eutactic. This caracterization has been extended in various cases,…
Minkowski's First Theorem and Dirichlet's Approximation Theorem provide upper bounds on certain minima taken over lattice points contained in domains of Euclidean spaces. We study the distribution of such minima and show, under some…
A finite Blaschke product, restricted to the unit circle, is a smooth covering map. The maximum and minimum values of the derivative of this map reflect the geometry of the Blaschke product. We identify two classes of extremal Blaschke…
The optimization of shape functionals under convexity, diameter or constant width constraints shows numerical challenges. The support function can be used in order to approximate solutions to such problems by finite dimensional optimization…
In this paper we study the area function of polygons, where the vertices are sliding along curves. We give geometric criteria for the critical points and determine also the Hesse matrix at those points. This is the starting point for a…
We use the intrinsic area to define a distance on the space of homothety classes of convex bodies in the $n$-dimensional Euclidean space, which makes it isometric to a convex subset of the infinite dimensional hyperbolic space. The ambient…
This paper consists of two halves. In the first half of the paper, we consider real-valued functions $f$ whose domain is the vertex set of a graph $G$ and that are Lipschitz with respect to the graph distance. By placing a uniform…
In mathematical modelling, the data and solutions are represented as measurable functions and their quality is oftentimes captured by the membership to a certain function space. One of the core questions for an analysis of a model is the…
We establish disc formulas for the Siciak-Zahariuta extremal function of an arbitrary open subset of complex affine space, generalizing Lempert's formula for the convex case. This function is also known as the pluricomplex Green function…