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math.MG2019
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…
math.MG2019
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…
math.MG2019
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…