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

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.

21 pages. arXiv admin note: text overlap with arXiv:1807.07936