A 𝐶^{𝑚} Whitney extension theorem for horizontal curves in the Heisenberg group

Pinamonti, Andrea; Speight, Gareth; Zimmerman, Scott

doi:10.1090/tran/7806

A $C^m$ Whitney extension theorem for horizontal curves in the Heisenberg group
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by Andrea Pinamonti, Gareth Speight and Scott Zimmerman PDF

Trans. Amer. Math. Soc. 371 (2019), 8971-8992 Request permission

Abstract:

We characterize those mappings from a compact subset of $\mathbb {R}$ into the Heisenberg group ${\mathbb {H}}^{n}$, which can be extended to a $C^{m}$ horizontal curve in $\mathbb {H}^{n}$. The characterization combines the classical Whitney conditions with an estimate comparing changes in the vertical coordinate with those predicted by the Taylor series of the horizontal coordinates.

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