Results 41 to 50 of about 95 (50)
Connections between metric differentiability and rectifiability
We combine Kirchheim's metric differentials with Cheeger charts in order to establish a non-embeddability principle for any collection $\mathcal C$ of Banach (or metric) spaces: if a metric measure space $X$ bi-Lipschitz embeds in some element in ...
Caamaño, Iván +4 more
core
The celebrated Johnson-Lindenstrauss lemma states that for all $\varepsilon \in (0,1)$ and finite sets $X \subseteq \mathbb{R}^N$ with $n>1$ elements, there exists a matrix $\Phi \in \mathbb{R}^{m \times N}$ with $m=\mathcal{O}(\varepsilon^{-2}\log n ...
Chiclana, Rafael +2 more
core
Geometric Property (T) and Kazhdan projections
We characterise Geometric Property (T) by the existence of a certain projection in the maximal uniform Roe algebra $C_{u,\max}^*(X)$, extending the notion of Kazhdan projection for groups to the realm of metric spaces. We also describe this projection in
Vergara, Ignacio
core +1 more source
Coarse entropy of metric spaces. [PDF]
Geom DedicGeller W, Misiurewicz M, Sawicki D.
europepmc +1 more source
Expanding Ricci solitons coming out of weakly PIC1 metric cones
Motivated by recent work of Deruelle-Schulze-Simon, we study complete weakly PIC1 Ricci flows with Euclidean volume growth coming out of metric cones. We show that such a Ricci flow must be an expanding gradient Ricci soliton, and as a consequence, any ...
Chan, Pak-Yeung +2 more
core
Hurewicz and Dranishnikov-Smith theorems for asymptotic dimension of countable approximate groups
We establish two main results for the asymptotic dimension of countable approximate groups. The first one is a Hurewicz type formula for a global morphism of countable approximate groups $f:(\Xi, \Xi^\infty) \to (\Lambda, \Lambda^\infty)$, stating that $\
Hartnick, Tobias, Tonić, Vera
core
Coarse embeddings of quotients by finite group actions
We prove that for a metric space $X$ and a finite group $G$ acting on $X$ by isometries, if $X$ coarsely embeds into a Hilbert space, then so does the quotient $X/G$.
Weighill, Thomas
core
On the weak$^*$ separability of the space of Lipschitz functions
We conjecture that whenever $M$ is a metric space of density at most continuum, then the space of Lipschitz functions is $w^*$-separable. We prove the conjecture for several classes of metric spaces including all the Banach spaces with a projectional ...
Candido, Leandro +2 more
core
Bi-Lipschitz embedding metric triangles in the plane
A 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
core
Rigidity of area non-increasing maps
In this work, we consider the area non-increasing map between manifolds with positive curvature. By exploring the strong maximum principle along the graphical mean curvature flow, we show that an area non-increasing map between certain positively curved ...
Lee, Man-Chun +2 more
core