Results 1 to 10 of about 31 (31)
Algebraic entropy of endomorphisms of M-sets
Topological Algebra and its Applications, 2021 The usual notion of algebraic entropy associates to every group (monoid) endomorphism a value estimating the chaos created by the self-map. In this paper, we study the extension of this notion to arbitrary sets endowed with monoid actions, providing ...
Zava Nicolò
doaj +1 more source
A Simple Proof of Dvoretzky-Type Theorem for Hausdorff Dimension in Doubling Spaces
Analysis and Geometry in Metric Spaces, 2022 The ultrametric skeleton theorem [Mendel, Naor 2013] implies, among other things, the following nonlinear Dvoretzky-type theorem for Hausdorff dimension: For any 0 < β < α, any compact metric space X of Hausdorff dimension α contains a subset which is ...
Mendel Manor
doaj +1 more source
On L1-Embeddability of Unions of L1-Embeddable Metric Spaces and of Twisted Unions of Hypercubes
Analysis and Geometry in Metric Spaces, 2022 We study properties of twisted unions of metric spaces introduced in [Johnson, Lindenstrauss, and Schechtman 1986], and in [Naor and Rabani 2017]. In particular, we prove that under certain natural mild assumptions twisted unions of L1-embeddable metric ...
Ostrovskii Mikhail I. +1 more
doaj +1 more source
Hyperbolic Metric Spaces and Stochastic Embeddings
Forum of Mathematics, SigmaStochastic embeddings of finite metric spaces into graph-theoretic trees have proven to be a vital tool for constructing approximation algorithms in theoretical computer science.
Chris Gartland
doaj +1 more source
Contractibility of boundaries of cocompact convex sets and embeddings of limit sets
Analysis and Geometry in Metric SpacesWe provide sufficient conditions as to when a boundary component of a cocompact convex set in a CAT(0){\rm{CAT}}\left(0)-space is contractible. We then use this to study when the limit set of a quasi-convex, codimension one subgroup of a negatively ...
Bregman Corey, Incerti-Medici Merlin
doaj +1 more source
Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups
Analysis and Geometry in Metric SpacesWe show that infinite cyclic subgroups of groups acting uniformly properly on injective metric spaces are uniformly undistorted. In the special case of hierarchically hyperbolic groups, we use this to study translation lengths for actions on the ...
Abbott Carolyn +3 more
doaj +1 more source
Fat minors cannot be thinned (by quasi-isometries)
Analysis and Geometry in Metric SpacesWe disprove the conjecture of Georgakopoulos and Papasoglu that a graph with no K-fat H minor is quasi-isometric to a graph with no H minor. On the other hand, we show that the following weakening holds: any graph with no K-fat H minor is quasi-isometric
Davies James +3 more
doaj +1 more source
Bi-Lipschitz embedding metric triangles in the plane
Analysis and Geometry in Metric SpacesA metric polygon is a metric space comprised of a finite number of closed intervals joined cyclically. The second-named author and Ntalampekos recently found a method to bi-Lipschitz embed an arbitrary metric triangle in the Euclidean plane with ...
Luo Xinyuan +2 more
doaj +1 more source
Some of the next articles are maybe not open access.
Transfinite Asymptotic Dimension and APD Profiles
Topology and Its Applications, 2021Takamitsu Yamauchi
exaly
On Coarse Directed Limits of Metric Spaces
Rocky Mountain Journal of Mathematics, 2023Chi-Keung Ng
exaly