Calculus of Variations and Geometric Measure Theory

A. Pinamonti - G. Speight - S. Zimmerman

Higher Order Whitney Extension and Lusin Approximation for Horizontal Curves in the Heisenberg Group

created by pinamonti on 10 Oct 2023
modified on 07 Jun 2024


Accepted Paper

Inserted: 10 oct 2023
Last Updated: 7 jun 2024

Journal: J. Math. Pures Appl.
Year: 2024


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.