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In the setting of horizontal curves in the Heisenberg group, we prove a$C^{m,\omega}$ finiteness principle, a $C^{m,\omega}$ Lusin approximationresult, a $C^{\infty}$ Whitney extension result, and a $C^{\infty}$ Lusinapproximation result. Combined with previous work, this completes the study ofWhitney extension and Lusin approximation for horizontal curves of class$C^{m}$, $C^{m,\omega}$, and $C^{\infty}$ in the Heisenberg group.

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