A $C^{m,ω}$ Whitney Extension Theorem for Horizontal Curves in the Heisenberg Group

We characterize which mappings from a compact subset of $\mathbb{R}$ into the Heisenberg group can be extended to a $C^{m,ω}$ horizontal curve for a given modulus of continuity $ω$. We motivate our characterization by showing that the $C^{m,ω}$ extension property fails if we instead use a more direct analogue of the conditions from the $C^{m}$ case.

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