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arXiv · 2505.14678

Directional Pliability, Whitney Extension, and Lusin Approximation for Curves in Carnot Groups

Gareth Speight·Scott Zimmerman
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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 $C^{1}$ horizontal curve in a set of positive measure.

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BibTeXRIS

Gareth Speight, Scott Zimmerman. 2025-05-20. Directional Pliability, Whitney Extension, and Lusin Approximation for Curves in Carnot Groups. https://arxiv.org/abs/2505.14678

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