Directional Pliability, Whitney Extension, and Lusin Approximation for Curves in Carnot Groups
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 C1 horizontal curve in a set of positive measure.
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