Published Paper

Inserted: 7 apr 2022
Last Updated: 28 feb 2025

Journal: The Journal of Geometric Analysis
Volume: 33
Pages: 21
Year: 2023
Links: Journal

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.

Keywords: Carnot, Whitney, Heisenberg

Download:

• A C@@m@w@ Whitney Extension Theorem for Horizontal Curves in the Heisenberg Group.pdf