4 citations · 5 across the 11 of their papers we have counts for
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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…
An implicit function theorem for Lipschitz mappings into metric spaces
Piotr Hajłasz, Scott Zimmerman
We prove a version of the implicit function theorem for Lipschitz mappings into arbitrary metric spaces. As long as the pull-back of the Hausdor…
A Whitney Extension Theorem for Horizontal Curves in the Heisenberg Group
Andrea Pinamonti, Gareth Speight, Scott Zimmerman
We characterize those mappings from a compact subset of into the Heisenberg group which can be extended to a horizontal curve in $\mathbb{H}^{…
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…