Related papers: On hyperballeans of bounded geometry
Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two…
We study Bowditch's notion of a coarse median on a metric space and formally introduce the concept of a coarse median structure as an equivalence class of coarse medians up to closeness. We show that a group which possesses a uniformly…
We consider the covering of a ball in certain normed spaces by its congruent subsets and show that if the finite number of sets is not greater than the dimensionality of the space, then the centre of the ball either belongs to the interior…
It is shown that for non-hyperbolic real quadratic polynomials topological and quasisymmetric conjugacy classes are the same. By quasiconformal rigidity, each class has only one representative in the quadratic family, which proves that…
In this paper it is proved that relative hyperbolicity is an invariant of quasi-isometry. As a byproduct of the arguments, simplified definitions of relative hyperbolicity are obtained. In particular we obtain a new definition very similar…
We study the geometry of warped cones over free, minimal isometric group actions and related constructions of expander graphs. We prove a rigidity theorem for the coarse geometry of such warped cones: Namely, if a group has no abelian…
We show that many graphs naturally associated to a connected, compact, orientable surface are hierarchically hyperbolic spaces in the sense of Behrstock, Hagen and Sisto. They also automatically have the coarse median property defined by…
We relate three classes of nonpositively curved metric spaces: hierarchically hyperbolic spaces, coarsely injective spaces, and strongly shortcut spaces. We show that every hierarchically hyperbolic space admits a new metric that is…
For a bornology $\mathcal B$ on a cardinal $\kappa$, we prove that the $\mathcal B$-macrocube is normal if and only if $\mathcal B$ has a linearly ordered base. As a corollary, we get that the hyperballean of bounded subsets of an…
We study bounded domains with certain smoothness conditions and the properties of their squeezing functions in order to prove that the domains are biholomorphic to the ball.
We study the intrinsic geometry of area minimizing (and also of almost minimizing) hypersurfaces from a new point of view by relating this subject to quasiconformal geometry. For any such hypersurface we define and construct a so-called…
There are three complete plane geometries of constant curvature: spherical, Euclidean and hyperbolic geometry. We explain how a closed oriented surface can carry a geometry which locally looks like one of these. Focussing on the hyperbolic…
A bounded automorphism of a field or a group with trivial approximate centre is definable. In an expansion of a field by a Pfaffian family F of additive endomorphisms such that algebraic closure in the expansion coincides with relative…
Hyperuniform states of matter are correlated systems that are characterized by an anomalous suppression of long-wavelength (i.e., large-length-scale) density fluctuations compared to those found in garden-variety disordered systems, such as…
We study several bialgebraic structures on boolean functions, that is to say maps defined on the set of subsets of a finite set $X$, taking the value $0$ on $\emptyset$. Examples of boolean functions are given by the indicator function of…
A bornology on a set $X$ is a family $\mathcal{B}$ of subsets of $X$ closed under taking subsets, finite unions and such that $\cup \mathcal{B}=X$. We prove that, for a bornology $\mathcal{B}$ on $X$, the following statements are…
We develop a direct method to recover an orthoalgebra from its poset of Boolean subalgebras. For this a new notion of direction is introduced. Directions are also used to characterize in purely order-theoretic terms those posets that are…
We give a complete description of the stable subset (the union of all backward orbit with bounded step) and of the pre-models of a univalent self-map $f: X\to X$, where $X$ is a Kobayashi hyperbolic cocompact complex manifold, such as the…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we…