7 papers · 1 filter
Quantitative decompositions of Lipschitz mappings into metric spaces
Guy C. David, Raanan Schul
We study the quantitative properties of Lipschitz mappings from Euclidean spaces into metric spaces. We prove that it is always possible to decompose the domain of such a mapping i…
Regular mappings and non-existence of bi-Lipschitz embeddings for slit carpets
Guy C. David, Sylvester Eriksson-Bique
We prove that the "slit carpet" introduced by Merenkov does not admit a bi-Lipschitz embedding into any uniformly convex Banach space. In particular, this includes any Euclidean sp…
On the Lipschitz dimension of Cheeger-Kleiner
Guy C. David
In a 2013 paper, Cheeger and Kleiner introduced a new type of dimension for metric spaces, the "Lipschitz dimension". We study the dimension-theoretic properties of Lipschitz dimen…
A sharp necessary condition for rectifiable curves in metric spaces
Guy C. David, Raanan Schul
In his 1990 Inventiones paper, P. Jones characterized subsets of rectifiable curves in the plane, using a multiscale sum of what is now known as Jones -numbers, numbers measurin…
A note on topological dimension, Hausdorff measure, and rectifiability
Guy C. David, Enrico Le Donne
The purpose of this note is to record a consequence, for general metric spaces, of a recent result of David Bate. We prove the following fact: Let be a compact metric space of…
Lipschitz and bi-Lipschitz maps from PI spaces to Carnot groups
Guy C. David, Kyle Kinneberg
This paper deals with the problem of finding bi-Lipschitz behavior in non-degenerate Lipschitz maps between metric measure spaces. Specifically, we study maps from (subsets of) Ahl…