2 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…