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For a real valued function defined on a compact set $K \subset \mathbb{R}^m$,the classical Whitney Extension Theorem from 1934 gives necessary andsufficient conditions for the existence of a $C^k$ extension to $\mathbb{R}^m$.In this paper, we prove a version of the Whitney Extension Theorem in the caseof $C^1$, horizontal extensions for mappings defined on compact subsets of$\mathbb{R}$ taking values in the Heisenberg Group $\mathbb{H}^n$.

The Whitney Extension Theorem for $C^1$, horizontal curves in the Heisenberg group