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arXiv · 1507.02240

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

Scott Zimmerman
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Abstract

For a real valued function defined on a compact set $K \subset \mathbb{R}^m$, the classical Whitney Extension Theorem from 1934 gives necessary and sufficient 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 case of $C^1$, horizontal extensions for mappings defined on compact subsets of $\mathbb{R}$ taking values in the Heisenberg Group $\mathbb{H}^n$.

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Scott Zimmerman. 2015-07-08. The Whitney Extension Theorem for $C^1$, horizontal curves in the Heisenberg group. https://arxiv.org/abs/1507.02240

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