Results 11 to 20 of about 95 (50)

Asymptotic dimension of fuzzy metric spaces

, 2021
In this paper, we define asymptotic dimension of fuzzy metric spaces in the sense of George and Veeramini. We prove that asymptotic dimension is an invariant in the coarse category of fuzzy metric spaces.
Grzegrzolka, Pawel
core   +1 more source

Contractibility of boundaries of cocompact convex sets and embeddings of limit sets

Analysis and Geometry in Metric Spaces
We 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 Spaces
We 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, Hagen Mark, Petyt Harry, Zalloum Abdul   +3 more
doaj   +1 more source

Weighted composition operators preserving various Lipschitz constants

, 2023
Let $\mathrm{Lip}(X)$, $\mathrm{Lip}^b(X)$, $\mathrm{Lip}^{\mathrm{loc}}(X)$ and $\mathrm{Lip}^\mathrm{pt}(X)$ be the vector spaces of Lipschitz, bounded Lipschitz, locally Lipschitz and pointwise Lipschitz (real-valued) functions defined on a ...
Liao, Ching-Jou, Liu, Chih-Neng, Liu, Jung-Hui, Wong, Ngai-Ching   +3 more
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Lipschitz geometry of pairs of normally embedded Hölder triangles [PDF]

, 2022
We consider a special case of the outer bi-Lipschitz classification of real semialgebraic (or, more general, definable in a polynomially bounded o-minimal structure) surface germs, obtained as a union of two normally embedded Hölder triangles.
Birbrair, Lev, Gabrielov, Andrei
core   +1 more source

From the coarse geometry of warped cones to the measured coupling of groups

, 2020
In this article, we prove that if two warped cones corresponding to two groups with free, isometric, measure-preserving, ergodic actions on two manifolds are quasi-isometric, then the corresponding groups are uniformly measured equivalent (UME).
Das, Kajal
core  

Rigidity of Lipschitz map using harmonic map heat flow

, 2022
Motivated by the Lipschitz rigidity problem in scalar curvature geometry, we prove that if a closed smooth spin manifold admits a distance decreasing continuous map of non-zero degree to a sphere, then either the scalar curvature is strictly less than ...
Lee, Man-Chun, Tam, Luen-Fai
core  

Semisimplicity manifesting as categorical smallness

, 2023
For a compact group $\mathbb{G}$, the functor from unital Banach algebras with contractive morphisms to metric spaces with 1-Lipschitz maps sending a Banach algebra $A$ to the space of $\mathbb{G}$-representations in $A$ preserves filtered colimits ...
Chirvasitu, Alexandru
core  

Intrinsically H\"older sections in metric spaces

, 2022
We introduce a notion of intrinsically H\"older graphs in metric spaces. Following a recent paper of Le Donne and the author, we prove some relevant results as the Ascoli-Arzel\`a compactness Theorem, Ahlfors-David regularity and the Extension Theorem ...
Di Donato, Daniela
core  

On stability of metric spaces and Kalton's property $Q$

, 2023
The first named author introduced the notion of upper stability for metric spaces as a relaxation of stability. The motivation was a search for a new invariant to distinguish the class of reflexive Banach spaces from stable metric spaces in the coarse ...
Baudier, F., Schlumprecht, Th., Zsák, A.   +2 more
core