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On the equivalence of derivatives for maps between Carnot groups
Scott Zimmerman
This paper gives an alternate, elementary proof of a result of Magnani: maps between Carnot groups that preserve horizontal curves and are continuously differential in horizontal d…
Bi-Lipschitz arcs in metric spaces with controlled geometry
Jacob Honeycutt, Vyron Vellis, Scott Zimmerman
We generalize a bi-Lipschitz extension result of David and Semmes from Euclidean spaces to complete metric measure spaces with controlled geometry (Ahlfors regularity and supportin…
A Whitney Extension Theorem for Horizontal Curves in the Heisenberg Group
Gareth Speight, Scott Zimmerman
We characterize which mappings from a compact subset of into the Heisenberg group can be extended to a horizontal curve for a given modulus of continuity …
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…
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…