Related papers: Non-Euclidean Analysis
We suggest a new approach to the study of relatively hyperbolic groups based on relative isoperimetric inequalities. Various geometric, algebraic, and algorithmic properties are discussed.
This paper formulates a conjectural description of of the space of weightless functions (see\cite{BK}) and raises a question about a possibility of extending such a description in a more general context.
We introduce a dimensional splitting method based on the intertwining property of the Radon transform, with a particular focus on its applications related to hyperbolic partial differential equations (PDEs). This dimensional splitting has…
There has been a recent surge of interest in using light and sound as platforms for studying non-Abelian physics. Through a kaleidoscope of physical effects, light and sound provide diverse ways to manipulate their degrees of freedom to…
In this paper, we study the structural stability of hyperbolic differential systems on Euclidean spaces using Liao theory.
In recent years we witness growing interest in using Real Analysis methods and results in the theory of nondivergence form partial differential equations (PDEs) and the goal of this article is to give a brief and concise introduction into…
We introduce a combined fully three-dimensional macroscopic/microscopic transport approach employing relativistic 3D-hydrodynamics for the early, dense, deconfined stage of the reaction and a microscopic non-equilibrium model for the later…
This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties…
The goal of this paper is to study two basic problems of hyperbolic geometry. The first problem is to compare the hyperbolic and Euclidean distances. The second problem is to find hyperbolic counterparts of some basic geometric…
The purpose of this note is to discuss examples of geometric transition from hyperbolic structures to half-pipe and Anti-de Sitter structures in dimensions two, three and four. As a warm-up, explicit examples of transition to Euclidean and…
Non-Euclidean geometry, discovered by negating Euclid's parallel postulate, has been of considerable interest in mathematics and related fields for the description of geographical coordinates, Internet infrastructures, and the general…
In this article we give evaluations of certain series of hyperbolic functions, using Jacobi elliptic functions theory. We also define some new functions that enable us to give characterization of not solvable class of series.
This work introduces a novel and general class of continuous transforms based on hierarchical Voronoi based refinement schemes. The resulting transform space generalizes classical approaches such as wavelets and Radon transforms by…
In this paper we continue the study of non-diagonalisable hyperbolic systems with variable multiplicity started by the authors in \cite{Garetto2018}. In the case of space dependent coefficients, we prove a representation formula for…
Global and local regularities of functions are analyzed in anisotropic function spaces, under a common framework, that of hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities…
The purpose of this paper is to study the notion of the quasihyperbolic volume and to find growth estimates for the quasihyperbolic volume of balls in a domain $G \subset {\mathbb R}^n\,$ in terms of the radii.
We study the moduli space of negatively curved metrics of a hyperbolic manifold.
A brief review on the recent theoretical progress in hot/dense QCD is given. Special emphasis is put on the non-perturbative aspects of QCD plasma and the modification of hadron proporties near the critical temperature of chiral transition.
Using the modern perspective of noncommutative algebraic geometry we survey some recent progress in the theory of stability conditions and moduli spaces with applications in hyperk\"ahler geometry and classical algebraic geometry.
We study the most elementary aspects of harmonic analysis on a homogeneous space of a deformation of the two-dimensional Euclidean group, admitting generalizations to dimensions three and four, whose quantum parameter has the physical…