3 papers
math.MG2026
A Lipschitz curve in a Carnot group that is purely unrectifiable by smooth horizontal curves
Gareth Speight, Scott Zimmerman
We construct a Lipschitz curve in the free Carnot group of step 3 with 2 generators that meets every horizontal curve in a set of measure zero. This shows that the $C^{1}_{…
math.DG2025
Directional Pliability, Whitney Extension, and Lusin Approximation for Curves in Carnot Groups
Gareth Speight, Scott Zimmerman
We show that, in arbitrary Carnot groups, pliability in a subset of directions is sufficient to guarantee the existence of a Whitney-type extension and a Lusin approximation for cu…
math.MG2023
Higher order Whitney extension and Lusin approximation for Horizontal curves in the Heisenberg group
Andrea Pinamonti, Gareth Speight, Scott Zimmerman
In the setting of horizontal curves in the Heisenberg group, we prove a finiteness principle, a Lusin approximation result, a Whitney extension res…