Related papers: Harmonic nets in metric spaces

We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which…

Symmetric homology is an analog of cyclic homology in which the cyclic groups are replaced by symmetric groups. The foundations for the theory of symmetric homology of algebras are developed in the context of crossed simplicial groups using…

Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…

Convergence spaces are a generalization of topological spaces. The category of convergence spaces is well-suited for Algebraic Topology, one of the reasons is the existence of exponential objects provided by continuous convergence. In this…

Motivated by recent work of Bukh and Nivasch on one-sided $\varepsilon$-approximants, we introduce the notion of \emph{weighted $\varepsilon$-nets}. It is a geometric notion of approximation for point sets in $\mathbb{R}^d$ similar to…

By a fixed continuous map from a $3$-space to itself, a knot in the $3$-space may be mapped to another knot in the $3$-space. We analyze possible knot types of them. Then we map a knot repeatedly by a fixed continuous map and analyze…

Associated to any finite metric space are a large number of objects and quantities which provide some degree of structural or geometric information about the space. In this paper we show that in the setting of subsets of weighted Hamming…

The first result in this study is a non-existence theorem for $\alpha-$harmonic mappings. Additionally, a direct connection between the $\alpha-$ harmonic and harmonic maps is made possible via conformal deformation. Second, the instability…

Real networks are finite metric spaces. Yet the geometry induced by shortest path distances in a network is definitely not its only geometry. Other forms of network geometry are the geometry of latent spaces underlying many networks, and…

By virtue of harmonic maps on two-dimensional spheres (S$^{2}$), a topological quantization in spacetime is proposed. The discrete character of all physical quantities follows naturally. A Schwarzschild black hole, non-black hole and…

Motivated by the theory of harmonic maps on Riemannian surfaces, conformal-harmonic maps between two Riemannian manifolds $M$ and $N$ were introduced in search of a natural notion of harmonicity for maps defined on a general even…

The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…

We study spaces of realisations of linkages (weighted graphs) whose underlying graph is a series parallel graph. In particular, we describe an algorithm for determining whether or not such spaces are connected.

We consider stabilities for the weighted length or energy functional of a discrete map from a finite weighted graph $(X,m_{E})$ into a smooth Riemannian manifold $(M,g)$. We prove the non-existence of a stable discrete minimal immersion or…

In a recent paper the first and the third authors introduced the notion of horizontal \alpha-harmonic map, with respect to a given C^1 planes distribution P_T on all R^m. The goal of this paper is to investigate compactness and quantization…

In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have…

Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…

Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…

This note tries to give an answer to the following question: Is there a sufficiently rich class of metric vector spaces such that sufficiently large spaces of continuous linear maps between them are metrizable?

We relate the existence problem of harmonic maps into $S^2$ to the convex geometry of $S^2$. On one hand, this allows us to construct new examples of harmonic maps of degree 0 from compact surfaces of arbitrary genus into $S^2$. On the…