2 citations · 2 across the 4 of their papers we have counts for
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Characterizing rectifiability via biLipschitz pieces of Lipschitz mappings on the space
Sean Li, Raanan Schul
We give the following characterization of rectifiable metric spaces. A metric space with positive lower Hausdorff density is rectifiable if and only if, for any subset and $f:F…
Notions of null sets in infinite-dimensional Carnot groups
Nathaniel Eldredge, Maria Gordina, Enrico Le Donne +1
We study several notions of null sets on infinite-dimensional Carnot groups. We prove that a set is Aronszajn null if and only if it is null with respect to measures that are convo…
The strong geometric lemma in the Heisenberg group
Vasileios Chousionis, Sean Li, Robert Young
We prove that in the first Heisenberg group, unlike Euclidean spaces and higher dimensional Heisenberg groups, the best possible exponent for the strong geometric lemma for intrins…
The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups
Vasileios Chousionis, Sean Li, Robert Young
We show that the --numbers of intrinsic Lipschitz graphs of Heisenberg groups are locally Carleson integrable when . Our technique relies on a recent Do…
Bi-Lipschitz embeddings of Heisenberg submanifolds into Euclidean spaces
Vasileios Chousionis, Sean Li, Vyron Vellis +1
The Heisenberg group equipped with a sub-Riemannian metric is one of the most well known examples of a doubling metric space which does not admit a bi-Lipschitz embedd…
The Traveling Salesman Theorem in Carnot Groups
Vasileios Chousionis, Sean Li, Scott Zimmerman
Let be any Carnot group. We prove that, if a subset of is contained in a rectifiable curve, then it satisfies Peter Jones' geometric lemma with some natur…