Related papers: Contraction of a Generalized Metric Structure

If the topology of the universe is compact we show how it significantly changes our assessment of the naturalness of the observed structure of the universe and the likelihood of its present state of high isotropy and near flatness arising…

We investigate gauge anomalies in the context of orbifold conformal field theories. Such anomalies manifest as failures of modular invariance in the constituents of the orbifold partition function. We review how this irregularity is…

In this paper, we study the topology associated to the fractal manifold model. It turns out that this topology is actually a family of topologies that gives to the fractal manifold a structure of variable topological space. Additionally, we…

Topography is the expression of both internal and external processes of a planetary body. Thus hypsometry (the study of topography) is a way to decipher the dynamic of a planet. For that purpose, the statistics of height and slopes may be…

It is shown that four-dimensional generalized symmetric spaces can be naturally equipped with some additional structures defined by means of their curvature operators. As an application, those structures are used to characterize generalized…

Skyrmions are important topologically non-trivial fields characteristic of models spanning scales from the microscopic to the cosmological. However, the Skyrmion number can only be defined for fields with specific boundary conditions,…

General relativity (GR) extensions based on renormalization group (RG) flows may lead to scale-dependent couplings with nontrivial effects at large distance scales. Here we develop further the approach in which RG effects at large distance…

Dilatations modify categories by imposing that some morphisms factorize through some others. This is formalized by a universal property. This text is devoted to introduce and study this construction. Examples of dilatations of categories…

We study non-compact scaling limits of uniform random planar quadrangulations with a boundary when their size tends to infinity. Depending on the asymptotic behavior of the boundary size and the choice of the scaling factor, we observe…

This paper studies a specific metric on plane curves that has the property of being isometric to classical manifold (sphere, complex projective, Stiefel, Grassmann) modulo change of parametrization, each of these classical manifolds being…

We propose to use the large-scale structure of the universe as a cosmic standard ruler, based on the fact that the pattern of galaxy distribution should be maintained in the course of time on large scales. By examining the scale-dependence…

The 'contracting boundary' of a proper geodesic metric space consists of equivalence classes of geodesic rays that behave like rays in a hyperbolic space. We introduce a geometrically relevant, quasi-isometry invariant topology on the…

Theories that attempt to explain cosmic acceleration by modifying gravity typically introduces a long-range scalar force that needs to be screened on small scales. One common screening mechanism is the chameleon, where the scalar force is…

In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…

The Lorentzian spacetime metric is replaced by an area metric which naturally emerges as a generalized geometry in quantum string and gauge theory. Employing the area metric curvature scalar, the gravitational Einstein-Hilbert action is…

We introduce a new definition of nonpositive curvature in metric spaces and study its relationship to the existing notions of nonpositive curvature in comparison geometry. The main feature of our definition is that it applies to all metric…

We present a construction, called the limit of a tree system of spaces (or, less formally, a tree of spaces). The construction is designed to produce compact metric spaces that resemble fractals, out of more regular spaces, such as closed…

This paper investigates spaces equipped with a family of metric-like functions satisfying certain axioms. These functions provide a unified framework for defining topology, uniformity, and diffeology. The framework is based on a family of…

In gravity theories that exhibit spontaneous scalarization, astrophysical objects are identical to their general relativistic counterpart until they reach a certain threshold in compactness or curvature. Beyond this threshold, they acquire…

Diversities have recently been developed as multiway metrics admitting clear and useful notions of hyperconvexity and tight span. In this note we consider the analytic properties of diversities, in particular the generalizations of uniform…