Related papers: Around distance-squared mappings
The article contains a brief description on the study of conformal scalar curvature equations, and discusses selected topics and questions concerning the equations in open spaces.
Consider an analytic map of a neighborhood of 0 in a vector space to a Euclidean space. Suppose that this map takes all germs of lines passing through 0 to germs of circles. Such a map is called rounding. We introduce a natural equivalence…
These are the notes from my courses on the arithmetic of quadratic forms.
This is an introductory article to the theory of multiple gaps.
This is a survey of results on random group presentations, and on random subgroups of certain fixed groups. Being a survey, this paper does not contain new results, but it offers a synthetic view of a part of this very active field of…
The article provides a brief survey of the mathematics of some of the newly being developed so called "hybrid" (also called "multi-physics" or "multi-wave") imaging techniques.
In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distance-regular graph. By using…
We survey several results known on sampling in computational geometry.
This paper is a survey of the relationship between labelled configuration spaces, mapping class groups with marked points and function spaces. In particular, we collect calculations of the cohomology groups for the mapping class groups of…
In this article a new upper bounds for the multiple trigonometrical integrals are found. The method of the work based on a new method of estimation for the areas of algebraic surfaces.
We study several geometric and analytic aspects of Dirac-harmonic maps with curvature term from closed Riemannian surfaces.
This article is aimed at presenting the Schr\"odinger problem and some of its connections with optimal transport. We hope that it can be used as a basic user's guide to Schr\"odinger problem. We also give a survey of the related literature.…
The aim of this survey is to present some aspects of multifractal analysis around the recently developed subject of multiple ergodic averages. Related topics include dimensions of measures, oriented walks, Riesz products etc.
In this survey, we give a short overview of the recent progress on the multidimensional L2 conjecture. It can also serve as an introduction to the subject.
We consider here square tilings of the plane. By extending the formalism introduced in [3] we build a correspondence between plane maps endowed with an harmonic vector and square tilings satisfying a condition of regularity. In the case of…
We study theoretical and computational aspects of the least squares fit (LSF) of circles and circular arcs. First we discuss the existence and uniqueness of LSF and various parametrization schemes. Then we evaluate several popular circle…
This paper provides a survey of spherical designs and their applications, with a particular emphasis on the perspective of ``numerical analysis''. A set \(X_N\) of \(N\) points on the unit sphere \(\mathbb{S}^d\) is called a…
We explain in some detail the geometric structure of spheres in any dimension. Our approach may be helpful for other homogeneous spaces (with other signatures) such as the de Sitter and anti-de Sitter spaces. We apply the procedure to the…
The aim of this paper is to revise the literature on different metric locations in the families of paths, cycles, trees and unicyclic graphs, as well as, provide several new results on that matter.
This paper is a survey on arc spaces, a recent topic in algebraic geometry and singularity theory. The geometry of the arc space of an algebraic variety yields several new geometric invariants and brings new light to some classical…