Results 11 to 20 of about 159 (44)

Sharp distortion growth for bilipschitz extension of planar maps

, 2012
This note addresses the quantitative aspect of the bilipschitz extension problem. The main result states that any bilipschitz embedding of $\mathbb R$ into $\mathbb R^2$ can be extended to a bilipschitz self-map of $\mathbb R^2$ with a linear bound on ...
Kovalev, Leonid V.
core   +1 more source

On the magnitude function of domains in Euclidean space

, 2020
We study Leinster's notion of magnitude for a compact metric space. For a smooth, compact domain $X\subset \mathbb{R}^{2m-1}$, we find geometric significance in the function $\mathcal{M}_X(R) = \mathrm{mag}(R\cdot X)$.
Gimperlein, Heiko, Goffeng, Magnus
core   +1 more source

Some remarks on generalized roundness

, 2007
By using the links between generalized roundness, negative type inequalities and equivariant Hilbert space compressions, we obtain that the generalized roundness of the usual Cayley graph of finitely generated free groups and free abelian groups of rank $
Jaudon, Ghislain
core   +2 more sources

Isospectral Alexandrov Spaces

, 2013
We construct the first non-trivial examples of compact non-isometric Alexandrov spaces which are isospectral with respect to the Laplacian and not isometric to Riemannian orbifolds. This construction generalizes independent earlier results by the authors
Engel, Alexander, Weilandt, Martin
core   +1 more source

Characterizations of Urysohn universal ultrametric spaces

Analysis and Geometry in Metric Spaces
In this article, using the existence of infinite equidistant subsets of closed balls, we first characterize the injectivity of ultrametric spaces for finite ultrametric spaces. This method also gives characterizations of the Urysohn universal ultrametric
Ishiki Yoshito
doaj   +1 more source

Some applications of Ball's extension theorem [PDF]

, 2006
We present two applications of Ball's extension theorem. First we observe that Ball's extension theorem, together with the recent solution of Ball's Markov type 2 problem due to Naor, Peres, Schramm and Sheffield, imply a generalization, and an ...
Mendel, Manor, Naor, Assaf
core  

Uniform estimates of nonlinear spectral gaps [PDF]

, 2015
By generalizing the path method, we show that nonlinear spectral gaps of a finite connected graph are uniformly bounded from below by a positive constant which is independent of the target metric space. We apply our result to an $r$-ball $T_{d,r}$ in the
Kondo, Takefumi, Toyoda, Tetsu
core  

The oscillation stability problem for the Urysohn sphere: A combinatorial approach [PDF]

, 2009
We study the oscillation stability problem for the Urysohn sphere, an analog of the distortion problem for $\ell_2$ in the context of the Urysohn space $\Ur$.
Abad, Jordi Lopez, Van Thé, Lionel Nguyen   +1 more
core   +2 more sources

Magnitude, diversity, capacities, and dimensions of metric spaces

, 2014
Magnitude is a numerical invariant of metric spaces introduced by Leinster, motivated by considerations from category theory. This paper extends the original definition for finite spaces to compact spaces, in an equivalent but more natural and direct ...
Meckes, Mark W.
core   +1 more source

Asymptotic dimension and uniform embeddings

, 2006
We show that the type function of a space with finite asymptotic dimension estimates its Hilbert (or any $l^p$) compression. The method allows to obtain the lower bound of the compression of the lamplighter group $Z\wr Z$, which has infinite asymptotic ...
Gal, S. R.
core   +2 more sources