Resumen de Lusin approximation and horizontal curves in Carnot groups

Gareth Speight

• We show that, given an absolutely continuous horizontal curve γ in the Heisenberg group, there is a C1 horizontal curve Γ such that Γ=γ and Γ′=γ′ outside a set of small measure. Conversely, we construct an absolutely continuous horizontal curve in the Engel group with no C1 horizontal approximation.