Higher order Whitney extension and Lusin approximation for horizontal curves in the Heisenberg group

In the setting of horizontal curves in the Heisenberg group, we prove a Cm,ω finiteness principle, a Cm,ω Lusin approximation result, a C∞ Whitney extension result, and a C∞ Lusin approximation result. Combined with previous work, this completes the study of Whitney extension and Lusin approximation for horizontal curves of class Cm, Cm,ω, and C∞ in the Heisenberg group.