Directional Pliability, Whitney Extension, and Lusin Approximation for Curves in Carnot Groups
Differential Geometry
2025-05-21 v1
Abstract
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 curves with tangent vectors in the same set of directions. We apply this to show that every horizontal curve in the Engel group must intersect a horizontal curve in a set of positive measure.
Cite
@article{arxiv.2505.14678,
title = {Directional Pliability, Whitney Extension, and Lusin Approximation for Curves in Carnot Groups},
author = {Gareth Speight and Scott Zimmerman},
journal= {arXiv preprint arXiv:2505.14678},
year = {2025}
}
Comments
22 pages