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arXiv · 2204.03544

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

Gareth Speight·Scott Zimmerman
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Abstract

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

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Gareth Speight, Scott Zimmerman. 2022-04-07. A $C^{m,\omega}$ Whitney Extension Theorem for Horizontal Curves in the Heisenberg Group. https://arxiv.org/abs/2204.03544

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