Revista Matemática Iberoamericana


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Volume 32, Issue 4, 2016, pp. 1423–1444
DOI: 10.4171/RMI/924

Published online: 2016-12-16

Lusin approximation and horizontal curves in Carnot groups

Gareth Speight[1]

(1) University of Cincinnati, USA

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.

Keywords: Carnot group, Heisenberg group, Engel group, horizontal curve, Lusin approximation, Whitney extension

Speight Gareth: Lusin approximation and horizontal curves in Carnot groups. Rev. Mat. Iberoam. 32 (2016), 1423-1444. doi: 10.4171/RMI/924