C. Gartland

activity

20162026

most citedPurely 1-unrectifiable metric spaces and locally flat Lipschitz functions

19 citations · 23 across the 14 of their papers we have counts for

collaborators

20 papers

math.FA2026

On complementation and $L$ -embedding of Lipschitz-free spaces in their biduals

Bruno M. Braga, Chris Gartland, Gilles Lancien +3

A closed subspace $E$ of a Banach space $F$ is \emph{ $L$ -embedded in $F$ } if there is a projection $P : F \to E$ such that $∥ x ∥ = ∥ P x ∥ + ∥ x - P x ∥$ for all $x \in F$ . We show that…

math.FA2026

On the $L$ -embeddability of Lipschitz-free spaces in their biduals

Bruno de Mendonça Braga, Chris Gartland, Gilles Lancien +3

A Banach space $X$ is $L$ -embedded in its bidual if there is a projection $P : X^{**} \to X$ such that $∥ x ∥ = ∥ P x ∥ + ∥ x - P x ∥$ for all $x \in X^{**}$ . We show that, as long as $X…

math.GR2026

Uniformly Lipschitz Hyperbolic Group Actions on $ℓ^{p}$

Chris Gartland, Tianyi Zheng

Let $Γ$ be a finitely generated hyperbolic group, and let $Q$ denote the conformal dimension of its Gromov boundary $\partial Γ$ . We prove that for every $p < \frac{Q}{Q - 1}$ , the gr…

math.FA2026

Expanders prevent Property (H)

Bruno de Mendonç Braga, Chris Gartland, Gilles Lancien +3

We show that if a sequence of expander graphs equi-coarsely embeds into a Banach space, then this Banach space fails Kasparov and Yu's Property (H). Consequently, no Banach space w…

math.GR2026

$L_{1}$ Actions and Embeddings of Property A Spaces

Chris Gartland, Ignacio Vergara, Tianyi Zheng

We provide several new characterizations of Property A for bounded degree graphs. In particular, we show that $(X, d)$ has Property A if and only if there is a proper gauge $ω$ such…

math.FA2026

$L_{1}$ -distortion of Earth Mover Distances and Transportation Cost Spaces on High Dimensional Grids

Chris Gartland, Mikhail Ostrovskii, Yuval Rabani +1

We prove that the distortion of any embedding into $L_{1}$ of the transportation cost space or earth mover distance over a $d$ -dimensional grid ${1, \dots m}^{d}$ is $Ω (lo g N)$ , wher…

math.FA2026★ 1 cited

Lower Estimates for $L_{1}$ -Distortion of Transportation Cost Spaces

Chris Gartland, Mikhail Ostrovskii

Quantifying the degree of dissimilarity between two probability distributions on a finite metric space is a fundamental task in Computer Science and Computer Vision. A natural diss…

math.FA2025

On the uniform continuity of homeomorphisms between the spheres of $ℓ_{\infty}^{k}$ and $ℓ_{1}^{k}$

Bruno de Mendonça Braga, Chris Gartland, Gilles Lancien +3

We consider the problem of whether there is a sequence of homeomorphisms $(F_{k})_{k}$ between the unit spheres of the $k$ -dimensional Banach spaces $ℓ_{\infty}^{k}$ and $ℓ_{1}^{k}$ whic…

math.FA2024★ 2 cited

Hyperbolic Metric Spaces and Stochastic Embeddings

Chris Gartland

Stochastic embeddings of finite metric spaces into graph-theoretic trees have proven to be a vital tool for constructing approximation algorithms in theoretical computer science. I…

math.FA2022

Lipschitz Functions on Unions and Quotients of Metric Spaces

David M. Freeman, Chris Gartland

Given a finite collection ${X_{i}}_{i \in I}$ of metric spaces, each of which has finite Nagata dimension and Lipschitz free space isomorphic to $L^{1}$ , we prove that their union has…

math.MG2022

$L_{1}$ -distortion of Wasserstein metrics: a tale of two dimensions

Florent P. Baudier, Chris Gartland, Thomas Schlumprecht

By discretizing an argument of Kislyakov, Naor and Schechtman proved that the 1-Wasserstein metric over the planar grid ${0, 1, \dots n}^{2}$ has $L_{1}$ -distortion bounded below by a…

math.MG2022

Lipschitz Functions on Quasiconformal Trees

David M. Freeman, Chris Gartland

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-Biq…

math.MG2021

Nilpotent groups and biLipschitz embeddings into $L^{1}$

Sylvester Eriksson-Bique, Chris Gartland, Enrico Le Donne +2

We prove that if a simply connected nilpotent Lie group quasi-isometrically embeds into an $L^{1}$ space, then it is abelian. We reach this conclusion by proving that every Carnot gr…

math.MG2021★ 1 cited

Umbel convexity and the geometry of trees

Florent P. Baudier, Chris Gartland

For every $p \in (0, \infty)$ , a new metric invariant called umbel $p$ -convexity is introduced. The asymptotic notion of umbel convexity captures the geometry of countably branching t…

math.MG2021★ 19 cited

Purely 1-unrectifiable metric spaces and locally flat Lipschitz functions

Ramón J. Aliaga, Chris Gartland, Colin Petitjean +1

We characterize compact metric spaces whose locally flat Lipschitz functions separate points uniformly as exactly those that are purely 1-unrectifiable, resolving a problem of Weav…

math.FA2020

Lipschitz Free Spaces over Locally Compact Metric Spaces

Chris Gartland

We prove that the Lipschitz free space over a certain type of discrete metric space has the Radon-Nikodým property. We also show that the Lipschitz free space over a complete, loca…

math.FA2019

Nondentable Sets in Banach Spaces

S. J. Dilworth, Chris Gartland, Denka Kutzarova +1

In his study of the Radon Nikodým property of Banach spaces, Bourgain showed (among other things) that in any closed, bounded, convex set $A$ that is nondentable, one can find a se…

math.MG2019

Estimates on the Markov Convexity of Carnot Groups and Quantitative Nonembeddability

Chris Gartland

We show that every graded nilpotent Lie group $G$ of step $r$ , equipped with a left invariant metric homogeneous with respect to the dilations induced by the grading, (this include…

math.MG2019

Thick Families of Geodesics and Differentiation

Chris Gartland

The differentiation theory of Lipschitz functions taking values in a Banach space with the Radon-Nikodým property (RNP), originally developed by Cheeger-Kleiner, has proven to be a…

math.MG2016

Quasiconformal mappings on the Grushin plane

Chris Gartland, Derek Jung, Matthew Romney

We prove that a self-homeomorphism of the Grushin plane is quasisymmetric if and only if it is metrically quasiconformal and if and only if it is geometrically quasiconformal. As t…

On complementation and L-embedding of Lipschitz-free spaces in their biduals

On the L-embeddability of Lipschitz-free spaces in their biduals

Uniformly Lipschitz Hyperbolic Group Actions on ℓp

Expanders prevent Property (H)

L1​ Actions and Embeddings of Property A Spaces

L1​-distortion of Earth Mover Distances and Transportation Cost Spaces on High Dimensional Grids

Lower Estimates for L1​-Distortion of Transportation Cost Spaces

On the uniform continuity of homeomorphisms between the spheres of ℓ∞k​ and ℓ1k​

Hyperbolic Metric Spaces and Stochastic Embeddings

Lipschitz Functions on Unions and Quotients of Metric Spaces

L1​-distortion of Wasserstein metrics: a tale of two dimensions

Lipschitz Functions on Quasiconformal Trees

Nilpotent groups and biLipschitz embeddings into L1

Umbel convexity and the geometry of trees

Purely 1-unrectifiable metric spaces and locally flat Lipschitz functions

Lipschitz Free Spaces over Locally Compact Metric Spaces

Nondentable Sets in Banach Spaces

Estimates on the Markov Convexity of Carnot Groups and Quantitative Nonembeddability

Thick Families of Geodesics and Differentiation

Quasiconformal mappings on the Grushin plane

On complementation and $L$ -embedding of Lipschitz-free spaces in their biduals

On the $L$ -embeddability of Lipschitz-free spaces in their biduals

Uniformly Lipschitz Hyperbolic Group Actions on $ℓ^{p}$

$L_{1}$ Actions and Embeddings of Property A Spaces

$L_{1}$ -distortion of Earth Mover Distances and Transportation Cost Spaces on High Dimensional Grids

Lower Estimates for $L_{1}$ -Distortion of Transportation Cost Spaces

On the uniform continuity of homeomorphisms between the spheres of $ℓ_{\infty}^{k}$ and $ℓ_{1}^{k}$

$L_{1}$ -distortion of Wasserstein metrics: a tale of two dimensions

Nilpotent groups and biLipschitz embeddings into $L^{1}$