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arXiv · 1807.07936

A $C^m$ Whitney Extension Theorem for Horizontal Curves in the Heisenberg Group

Andrea Pinamonti·Gareth Speight·Scott Zimmerman
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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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Andrea Pinamonti, Gareth Speight, Scott Zimmerman. 2018-07-20. A $C^m$ Whitney Extension Theorem for Horizontal Curves in the Heisenberg Group. https://arxiv.org/abs/1807.07936

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