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arXiv · 2310.06953

Higher order Whitney extension and Lusin approximation for Horizontal curves in the Heisenberg group

Andrea Pinamonti·Gareth Speight·Scott Zimmerman
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Abstract

In the setting of horizontal curves in the Heisenberg group, we prove a $C^{m,\omega}$ finiteness principle, a $C^{m,\omega}$ Lusin approximation result, a $C^{\infty}$ Whitney extension result, and a $C^{\infty}$ Lusin approximation result. Combined with previous work, this completes the study of Whitney extension and Lusin approximation for horizontal curves of class $C^{m}$, $C^{m,\omega}$, and $C^{\infty}$ in the Heisenberg group.

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Andrea Pinamonti, Gareth Speight, Scott Zimmerman. 2023-10-10. Higher order Whitney extension and Lusin approximation for Horizontal curves in the Heisenberg group. https://arxiv.org/abs/2310.06953

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