# Lusin Approximation and Horizontal Curves in Carnot Groups

**preprint**
**year:** 2014

**abstract:** We show that, given an absolutely continuous horizontal curve $\gamma$ in the Heisenberg group, there is a $C^{1}$ horizontal curve $\Gamma$ such that $\Gamma=\gamma$ and $\Gamma'=\gamma'$ outside a set of small measure. Conversely, we construct an absolutely continuous horizontal curve in the Engel group with no $C^{1}$ horizontal approximation.

The paper is available on the
cvgmt preprint server.