相关论文: Isometric structure of transportation cost spaces …

The present paper deals with some structural properties of transportation cost spaces, also known as Arens-Eells spaces, Lipschitz-free spaces and Wasserstein spaces. The main results of this work are: (1) A necessary and sufficient…

The paper is devoted to the geometry of transportation cost spaces and their generalizations introduced by Melleray, Petrov, and Vershik (2008). Transportation cost spaces are also known as Arens-Eells, Lipschitz-free, or Wasserstein $1$…

This work aims to establish new results pertaining to the structure of transportation cost spaces. Due to the fact that those spaces were studied and applied in various contexts, they have also become known under different names such as…

Main results: (a) If a metric space contains $2n$ elements, the transportation cost space on it contains a $1$-complemented isometric copy of $\ell_1^n$. (b) An example of a finite metric space whose transportation cost space contains an…

We study transportation cost spaces over finite metric spaces, also known as Lipschitz free spaces. Our work is motivated by a core problem posed by S. Dilworth, D. Kutzarova and M. Ostrovskii, namely, find a condition on a metric space $M$…

This article is a continuation of our article in [Canad. J. Math. Vol. 72 (3), (2020), pp. 774--804]. We construct orthogonal bases of the cycle and cut spaces of the Laakso graph $\mathcal{L}_n$. They are used to analyze projections from…

These notes present a basic survey on Transportation cost spaces (aka Lipschitzfree spaces, Wasserstein spaces) and their bi-Lipschitz and linear embeddings into $L_1$ spaces. To make these notes as self-contained as possible, we added the…

This paper initiates the study of the structure of a new class of $p$-Banach spaces, $0<p<1$, namely the Lipschitz free $p$-spaces (alternatively called Arens-Eells $p$-spaces) $\mathcal{F}_{p}(\mathcal{M})$ over $p$-metric spaces. We…

The paper starts with discussion of applications of cycle spaces to transportation cost. After a short survey of the known results on cycle spaces, we turn to the study of minimal projections onto cycle spaces in the corresponding…

In this note we study the structure of Lipschitz-free Banach spaces. We show that every Lipschitz-free Banach space over an infinite metric space contains a complemented copy of $\ell_1$. This result has many consequences for the structure…

We study a non-archimedean (NA) version of transportation problems and introduce naturally arising ultra-norms which we call Kantorovich ultra-norms. For every ultra-metric space and every NA valued field (e.g., the field $\mathbb Q_{p}$ of…

We describe surjective linear isometries and linear isometry groups of a large class of Lipschitz-free spaces that includes e.g. Lipschitz-free spaces over any graph. We define the notion of a Lipschitz-free rigid metric space whose…

Using tools from the theory of optimal transport, we establish several results concerning isometric actions of amenable topological groups with potentially unbounded orbits. Specifically, suppose $d$ is a compatible left-invariant metric on…

Optimal transport is widely used in pure and applied mathematics to find probabilistic solutions to hard combinatorial matching problems. We extend the Wasserstein metric and other elements of optimal transport from the matching of sets to…

This article continues the investigation of the tracial geometry of classifiable $\mathrm{C}^*$-algebras that have real rank zero and stable rank one. Using the language of optimal transport, we describe several situations in which the…

We consider Lipschitz- and Arens-Eells-type function spaces constructed for magnetic graphs, which are adapted to this setting from the area of optimal transport on discrete spaces. After establishing the duality between these spaces, we…

In this paper we develop the metric theory for the outer space of a free product of groups. This generalizes the theory of the outer space of a free group, and includes its relative versions. The outer space of a free product is made of…

Main results of the paper: (1) For any finite metric space $M$ the Lipschitz free space on $M$ contains a large well-complemented subspace which is close to $\ell_1^n$. (2) Lipschitz free spaces on large classes of recursively defined…

Let $\mathcal{P}$ be a class of Banach spaces and let $T=\{T_\alpha\}_{\alpha\in A}$ be a set of metric spaces. We say that $T$ is a set of {\it test-spaces} for $\mathcal{P}$ if the following two conditions are equivalent: (1)…

We consider the problem of optimal transportation with general cost between a empirical measure and a general target probability on R d , with d $\ge$ 1. We extend results in [19] and prove asymptotic stability of both optimal transport…