Related papers: Lipschitz Free Spaces over Locally Compact Metric …
Inspired by the work of G. Lu on pseudo symplectic capacities we obtain several results on the Gromov width and the Hofer--Zehnder capacity of Hermitian symmetric spaces of compact type. Our results and proofs extend those obtained by Lu…
An infinite structure has the finite length property (over a given field) if, for each of its finite powers, chains of equivariant subspaces in the corresponding free vector space are bounded in length. Prior work showed that the countable…
In this note we show how to adjust some proofs of Koskela et. al 2003 and Jiang 2011 in order to show that in certain spaces $(X,d,\mu)$, like $RCD(K,N)$-spaces, every Sobolev function with local $L^{p}$-Laplacian and $p>\dim\mu$ is locally…
The celebrated Josefson-Nissenzweig theorem implies that for a Banach space $C(K)$ of continuous real-valued functions on an infinite compact space $K$ there exists a sequence of Radon measures $\langle\mu_n\colon\ n\in\omega\rangle$ on $K$…
We give necessary and sufficient conditions for a Banach space $X$ having the Radon-Nikod\'{y}m property in terms of polynomial spline sequences.
We prove that in a Euclidean space of dimension at least two, there exists a compact set of Lebesgue measure zero such that any real-valued Lipschitz function defined on the space is differentiable at some point in the set. Such a set is…
In this paper we extend the theory of Henstock-Orlicz spaces with respect to vector measure. We study the integral representation of operators. Lastly we study Uniformly convexity, reflexivity and the Radon-Nikodym property of the…
We characterize cofinally Bourbaki quasi-complete metric spaces and their completions in terms of certain Lipschitz-type functions. To this end, we introduce and study a new class of functions, namely strongly uniformly locally Lipschitz…
We show that compact Riemannian manifolds, regarded as metric spaces with their global geodesic distance, cannot contain a number of rigid structures such as (a) arbitrarily large regular simplices or (b) arbitrarily long sequences of…
The paper is concerned with b-metric and generalized b-metric spaces. One proves the existence of the completion of a generalized b-metric space and some fixed point results. The behavior of Lipschitz functions on b-metric spaces of…
In this paper, we give a generalisation of Gromov's compactness theorem for metric spaces, more precisely, we give a compactness theorem for the space of distance measure spaces equipped with a \emph{generalised…
We study the usual notion of Scott rank but in the setting of Polish metric spaces. The signature consists of distance relations: for each rational $q > 0$, there is a relation $R_{<q}(x,y)$ stating that the distance of $x$ and $y $ is less…
We study locally compact metric spaces that enjoy various forms of homogeneity with respect to M\"obius self-homeomorphisms. We investigate connections between such homogeneity and the combination of isometric homogeneity with…
We determine the local geometric structure of two-dimensional metric spaces with curvature bounded above as the union of finitely many properly embedded/branched immersed Lipschitz disks. As a result, we obtain a graph structure of the…
On complete metric spaces that support doubling measures, we show that the validity of a Rademacher theorem for Lipschitz functions can be characterised by Keith's "Lip-lip" condition. Roughly speaking, this means that at almost every…
The goal of this note is to prove the Half Space Property for RCD(0,N) spaces, namely that if (X,d,m) is a parabolic RCD(0,N) space and $ C \subset X \times \mathbb{R}$ is locally the boundary of a perimeter minimizing set and it is…
We show that given a compact group $G$ acting continuously on a metric space $M$ by bi-Lipschitz bijections with uniformly bounded norms, the Lipschitz-free space over the space of orbits $M/G$ (endowed with Hausdorff distance) is…
We compare several versions of the quantitative Schur property of Banach spaces. We establish their equivalence up to multiplicative constants and provide examples clarifying when the change of constants is necessary. We also give exact…
We first identify (up to linear isomorphism) the Lipschitz free spaces of quasiarcs. By decomposing quasiconformal trees into quasiarcs as done in an article of David, Eriksson-Bique, and Vellis, we then identify the Lipschitz free spaces…
Let X,Y be two Banach spaces ; in the first part of this work, we show that K(X,Y) contains a complemented copy of c0 if Y contains a copy of c0 and each bounded sequence in Y has a subsequece which is w* convergente. Afterward we obtain…